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This article considers the problem of finite-time command-filtered control for switched nonlinear systems with input quantization and output constraints. The unmeasurable state is estimated by designing a switched state observer. During the design process, to overcome the chattering problem effectively, the hysteresis quantization is designed as two bounded nonlinear functions. Furthermore, in order to restrict the output to an expected range, the barrier Lyapunov function approach is introduced. The "explosion of complexity" and the error compensation problems in the backstepping design are solved by using a finite-time command-filtered approach. A first-order Levant differentiator is used instead of the general command filter in this paper, which can not only filter the intermediate signals accurately to get the differential signals, but also ensure the finite-time stability of the filter. Stability of the closed-loop system in the sense of semi-global practical finite-time stability (SGPFS) is proved by exploring a multiple Lyapunov functions approach. Finally, a simulation example is provided to verify the validity of the presented control method. [ABSTRACT FROM AUTHOR]

This paper discusses the congestion control challenges in a network employing multi-bottleneck Transmission Control Protocol/Active Queue Management (TCP/AQM). The study specifically focuses on networks characterized by input nonlinearity and unknown disturbances. We regard the network as a whole, and consider the influence between multiple nodes and unknown disturbance, a dynamic model of multi-bottleneck network is established. And the impact of dead zone and saturation on the system is taken into account for the first time in the model, the builded TCP/AQM model is more practicable. Based on the characteristics of fuzzy logic systems (FLS), combined with backstepping technology and Lyapunov function, an adaptive congestion control algorithm is designed to make full use of the link resources of each node and improve the network utilization. Ultimately, the proposed algorithm's efficacy and superiority are substantiated through simulation. [ABSTRACT FROM AUTHOR]

Correction to the articles "Stability of Nonlinear 2D Systems Described by the Continuous-Time Roesser Model" and "Stabilization of Differential Repetitive Processes" published in the previous issue of the journal is presented.

This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the threshold dynamics of impact media reaction diffusion system is also given and the Kuratowski measure κ of non-compactness is also considered. In addition, assume the spatial environment is homogeneous, it is shown that the unique endemic equilibrium of the system is global stability by constructing suitable Lyapunov function. Finally, we discuss the asymptotic profile of the system when the diffusion rate of the susceptible (infected) individuals for the system tends to zero or infinity. The main results show that the activities of infected individuals can only be at low risk, and then the virus eventually will be extinct, that is, to control the entry of viruses from abroad and increase the detection of domestic viruses. Finally, some numerical simulations are worked out to confirm the results obtained in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic tracking problem for a class of second-order electromagnetic micromirror model with output performance constraints and anomaly control, which is subject to model parameter uncertainties and external disturbances. Specifically, this paper formulates the trajectory tracking control problem of an electromagnetic micromirror as a closed-loop control trajectory tracking problem based on the general solution framework of output regulation. Moreover, the extended internal model is introduced to reformulate the closed-loop control problem into a state stabilization problem of the augmented system. Based on the augmented system, an internal model backstepping controller is proposed by integrating the barrier Lyapunov Functions (BLF) and the Nussbaum gain function with the backstepping structure.This controller not only satisfies the output performance constraints of the micromirror, but also maintains the control performance in anomalous control situations. The final performance simulation demonstrates the efficacy of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of spacing control between adjacent trains in train formation and proposes a distributed train-formation speed-convergence cooperative-control algorithm based on barrier Lyapunov function. Considering practical limitations such as communication distance and bandwidth constraints during operation, not all trains can directly communicate with the leader and obtain the expected trajectory it sends, making it difficult to maintain formation consistency as per the predetermined ideal state. Furthermore, to address the challenge of unknown external disturbances encountered by trains during operation, this paper designs a distributed observer deployed on each train in the formation. This observer can estimate and dynamically compensate for unknown reference trajectories and disturbances solely based on the states of adjacent trains. Additionally, to ensure that the spacing between adjacent trains remains within a predefined range, a safety hard constraint, this paper encodes the spacing hard constraint using barrier Lyapunov function. By integrating nonlinear adaptive control theory to handle model parameter uncertainties, a barrier Lyapunov function-based adaptive control method is proposed, which enables all trains to track the reference trajectory while ensuring that the spacing between them remains within the preset interval, therefore guaranteeing the asymptotic stability of the closed-loop system. Finally, a practical example using data from the Guangzhou Metro Line 22, specifically the route from Shiguang Road Station to Chentougang Station over three stations and two sections, is utilized to validate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, some less conservative sufficient conditions for uniform exponential stability, local uniform exponential stability and uniform practical exponential stability of nonlinear time-varying systems on time scales are proposed. Compared with the traditional exponential stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. The main tools used are some Gronwall's inequalities on time scales. Two examples are also included to verify the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time boundedness problem of switched linear systems under periodically intermittent control. Sufficient conditions are established to guarantee finite-time boundedness or finite-time stability of switched linear systems under periodically intermittent control. The proof procedures are implemented successfully resorting to piecewise Lyapunov functions. Based on the linear matrix inequality technique, the conditions are casted into a convex optimisation problem and therefore, they can be efficiently handled. The method proposed in this paper is a much potentially useful one in practice because of its economical and efficient nature that is easy to employ. Finally, two examples are given to express the validity and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive consensus with limited information for a class of uncertain nonlinear multi-agent systems (MASs). The limited information, meaning the incomplete information transmitted between agents, stems from nonzero-kernel weight matrices of communication networks, which deserves concerns owing to its practical interest such as in privacy preserving and information compression. Apart from the limited/incomplete information, the paper considers nonlinear MASs with large uncertainties (without known upper bounds). This is essentially different from the existing results of linear systems and poses challenges for the design and analysis of adaptive consensus. As for fully distributed protocol design, dynamic high gains are introduced to compensate for the system uncertainties and for the unavailable global graph information. In closed-loop consensus analysis, a new Lyapunov function is constructed by utilising weight and incidence matrices instead of Laplacian matrix. It turns out that the designed protocol can guarantee the boundedness of closed-loop MASs signals and the convergent consensus. Two numerical examples are given to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when Δ < 0 ( Δ appears in Section 3), the three classes I t , M t , and R t appearing in the model go extinct at an exponential rate, and the susceptible class S t almost surely converges to the solution of the boundary equation exponentially. When Δ > 0 , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of Δ = 0 under some conditions. Some examples were listed to confirm the obtained results. The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when ( appears in Section 3), the three classes , , and appearing in the model go extinct at an exponential rate, and the susceptible class almost surely converges to the solution of the boundary equation exponentially. When , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of under some conditions. Some examples were listed to confirm the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different Φ-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the asynchronous control problem is investigated and a multiple convex Lyapunov functions (MCLF) approach is introduced for a class of discrete-time switched linear systems under the Φ-dependent integrated dwell time (ΦDIDT) switching strategy. For the problem of asynchronous switching, this paper considers that Lyapunov functions may jump when the subsystem switches or the controller changes. Thus, the constructed MCLF is dependent on both the asynchronous interval and the synchronous interval, and the synchronous interval is divided into the convex interval and non-convex interval parts. Some sufficient conditions of stability with Linear matrix inequality (LMI) forms are obtained, and the asynchronous controller is designed to guarantee the globally uniform exponential stability of the system under study. In addition, the proposed method can degenerate to the existing methods to deal with the asynchronous control problem. Finally, a numerical example illustrates the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the fractional exponential stability of bidirectional associative memory (BAM) neural networks with conformable derivative. Applying the contraction mapping theorem existence and uniqueness of the equilibrium is studied. Furthermore, an appropriate Lyapunov function is stated to get exponential stability. Numerical examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

This paper investigates the problem of exponential H ∞ output control for switching fuzzy systems, considering both impulse and non-impulse scenarios. Unlike previous research, where the average dwell time (ADT: τ a ) and the upper bound of inter-event intervals (IEIs: T) satisfy the condition τ a ≥ ln μ + (α + β) T α = ln μ + β T α + T , implying that frequent switching is difficult to achieve, this paper demonstrates that by adopting the mode-dependent event-triggered mechanism (ETM) and a switching law, frequent switching is indeed achieved. Moreover, the question of deriving the normal L 2 norm constraint is solved through the ADT method, although only a weighted L 2 norm constraint was obtained previously. Additionally, by constructing a controller-mode-dependent Lyapunov function and adopting logarithmic quantizers, the sufficient criteria of exponential H ∞ output control problem are presented. The validity of established results is demonstrated by a given numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results. [ABSTRACT FROM AUTHOR]

This paper discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability of general types of impulsive nonlinear systems. A controller that does not require a sign function is then proposed to ensure that the synchronization error converges to zero within a predetermined time. The controllerdesigned in this paper serves the additional purpose of preventing the use of an unreliable inequality in the course of proving the main results. Next, to guarantee FXT and PDT synchronization of the drive–response systems, this paper employs the Lyapunov function method and derives sufficient conditions. Finally, a numerical simulation is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear timevarying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process. [ABSTRACT FROM AUTHOR]

For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader's attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient "few controlling many" paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. [ABSTRACT FROM AUTHOR]

This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average l-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period l. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models. [ABSTRACT FROM AUTHOR]

This paper studies the switching topologies and tracking agent replacements for a class of nonlinear multi-agent systems with external disturbances. In particular, it is assumed that a number of monitoring agents are randomly deployed in a two-dimensional space. The agents are committed to tracking any intrusion targets in this area. When one of the following agents exits tracking for some reasons, the agent closer to the target joins the tracking team to ensure the number of tracking agents does not change. In order to achieve the successful tracking of the target, this paper designs a sliding mode controller for the relay multi-agent system with tracking agent replacements. Furthermore, an adaptive law is proposed to estimate the upper bound of disturbance in the relay tracking process. Next, the stability of the overall system will be analysed by applying the multiple Lyapunov function method based on the average dwell time. Finally, the effectiveness of the tracking strategy is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies several problems related to quadratic matrix inequalities (QMIs), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, or bounded or has a nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured"" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMIs can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller and also leads to explicit formulas for data-guided feedback gains. [ABSTRACT FROM AUTHOR]

In this paper, we study the global output feedback stabilization (GOFS) of nonlinear systems with unknown functions (UFs). Firstly, a lemma is introduced to solve UFs, which avoids the shortcomings of the approximate algorithms. At the same time, this lemma avoids the assumptions of UFs, thus reducing the conservatism of the algorithms. Secondly, based on Lyapunov function analysis, the controller is designed, which solves the GOFS problem of the controlled system. This control algorithm adopts nonbackstepping, so it avoids the complicated calculation of backstepping. Finally, the control algorithm is applied to the Duffing system to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper deals with the application of a fuzzy-logic-based controller for a drive with a BLDC motor. Two main aspects of the work are presented in this paper. The first of them is focused on the design process of the fuzzy model. For this purpose, the rules of the applied fuzzy system are defined according to the Lyapunov function. The gain coefficients of the controller are optimized using the Chameleon Swarm Algorithm. Various issues and aspects were analyzed in the simulation tests (robustness against parameter changes, the influence of the controller parameters on the precision of control, stages of optimization, etc.). The presented work confirms the assumptions regarding precision and stable operation (also in the presence of changes in the object parameters—the mechanical time constants of the engine) in connection with the applied fuzzy speed controller. Moreover, the second part of the manuscript presents the low-cost power electronic device developed for laboratory tests. It uses STM32 ARM-based microcontrollers (state variable measurement, control algorithm calculation, control signal generation) and a Raspberry Pi 4B microcomputer (control application—reference value and parameter definition). The experiment performed for the control structure—an electric drive with a BLDC motor—verified the theoretical considerations. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finite-time robust stabilization of inertial delayed neural networks with external disturbances. The finite-time stability research of inertial neural networks can be applied to important fields such as secure communication, so it has great significant research value. However, up to now, there are few previous studies on the finite-time stability of inertial neural networks, thus this paper makes up for this gap. Based on the actual communication networks, we improve the model of inertial neural networks, adding uncertainties and external disturbances. Unlike many previous papers based on scalar sign function, this paper introduces vector sign function, combines the constructed Lyapunov function, some inequality conditions, and related lemmas to design two effective controllers composed of U 1 (t) and U 2 (t) , which can handle uncertainties and external disturbances of the neural networks well, and realize finite-time robust stability of the neural networks with external disturbances. In addition, the theoretical part of this paper estimates an upper bound on the settling time for the system to reach stability. Under the conditions of a certain strategy, we further optimize the extremes of the settling time so that the system reaches stability in a shorter time. Our results improve and extend some recent works. Finally, two examples are given to verify the validity and correctness of the designed controllers by numerical simulations using MATLAB tool. [ABSTRACT FROM AUTHOR]

In this paper, a system of coupled quasi-linear and linear wave equations with a finite memory term is concerned. By constructing an appropriate Lyapunov function, we prove that the total energy associated with the system is stable under suitable conditions on memory kernel. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem of a class of linear multi-agent systems is analysed. In our model, switching between subnetworks and competition between agents is considered simultaneously.We suppose that all subnetworks cannot achieve a consensus and switching signal has a minimum dwell time. By using the time-dependent quadratic Lyapunov function and the average dwell time method, a consensus condition of switched networks is obtained. By using the sum of squares (SOS) programming in the software package SOSTOOLS of Matlab, these resulting conditions can be implemented. The results obtained are also extended to uncertain linear multi-agent systems. Finally, a simulation example is given to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

Summary This paper addresses the guaranteed performance control problem for a class of singular switched positive systems, where the switching signal is subject to a state‐dependent process. Firstly, the causality, regularity, positivity, and asymptotical stability of the considered systems are discussed. In order to prevent the occurrence of data collisions and reduce the consumption of communication resources, the event‐triggered (E‐T) mechanism is applied. This is one of the initial attempts to introduce the E‐T scheme for such special systems. Besides, an asynchronous nonfragile controller under the E‐T scheduling scheme is designed to make certain that the resulting closed‐loop systems are causal, regular, positive, asymptotically stable, and have a guaranteed performance value J∗$$ {J}^{\ast } $$. Through the application of the co‐positive Lyapunov function method and the min‐projection strategy, the corresponding sufficient conditions are given in the form of linear programming (LP). Finally, the effectiveness of the controller proposed in this paper is verified via two simulation examples. [ABSTRACT FROM AUTHOR]

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some suffcient conditions for ensuring pth moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coeffscients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples. [ABSTRACT FROM AUTHOR]

This paper dealt with a laminated beam system along with structural damping, past history, distributed delay, and in the presence of both temperatures and micro-temperatures effects. The damping terms left the system dissipative. Employing the semigroup approach, we established the existence and uniqueness of the solution. Additionally, with the help of convenient assumptions on the kernel, we demonstrated a general decay result for the solution of the considered system, with no constraints regarding the speeds of wave propagation. The main aim was to address how specific behaviors of the system were related to memory and delays. We aimed to investigate the joint impact of an infinite memory, distributed delay and micro-temperature effects on the system. We found a new relationship between the decay rate of solution and the growth of g at infinity. The objective was to find studies that use no-trivial results and their applications to relevant problems from mathematical physics. [ABSTRACT FROM AUTHOR]

This paper primarily focused on analyzing a stochastic SVIR epidemic model that incorporates Levy noises. The population may be divided into four distinct compartments: vulnerable class (S), vaccinated individuals (V), infected individuals (I), and recovered individuals (R). To achieve this, we chose existing and unique techniques as the most feasible solution. In the nexus, the stochastic model was theoretically analyzed using a suitable Lyapunov function. This analysis broadly covered the existence and uniqueness of the non-negative solution, as well as the dynamic properties related to both the disease-free equilibrium and the endemic equilibrium. In order to eradicate diseases, a stochastic threshold value denoted as "R0" was used to determine if they may be eradicated. If R0 < 1; it means that the illnesses have the potential to become extinct. Moreover, we provided numerical performance results of the proposed model using the artificial neural networks technique combined with the Bayesian regularization method. We firmly believe that this study will establish a solid theoretical foundation for comprehending the spread of an epidemic, the implementation of effective control strategies, and addressing real-world issues across various academic disciplines. [ABSTRACT FROM AUTHOR]

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers. [ABSTRACT FROM AUTHOR]

Using the Khatri-Rao product, we presented new characterizations for the common Lyapunov diagonal stability for a family of real matrices A. For special partitions a, we used the notion of Pα-sets and common α-scalar Lyapunov stability to formulate further characterizations. Furthermore, generalizations of these results to the common α-scalar Lyapunov stability were developed. Our goal of this paper was to unify and enhance relevant work. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the instability issues of stochastic differential systems with impulsive effects. Definitions of instability including almost sure exponential instability, pth moment exponential instability and pth moment instability are given. By using the Lyapunov functions, the comparison theorem and the average impulsive interval condition, several instability criteria are established. Three examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a new method for regional stabilization of discrete-time nonlinear systems by static output feedback based on polynomial Lyapunov functions. The considered class of nonlinear systems subject to time-varying parameters can be described by difference-algebraic representation and an equivalent polytopic model is obtained, making it possible to apply Lyapunov theory and linear matrix inequality-based tool. In this sense, a convex optimization problem in terms of LMI is provided to guarantee the closed-loop system's robust stabilization and to enlarge the estimated domain of attraction (DoA). The proposed control design is a one-step approach that can be applied to systems with nonlinear output matrices. It requires no iterative algorithms or congruence transformation, and auxiliary decision variables are introduced only aiming at less conservative results. Besides that, the use of polynomial Lyapunov functions allows us to obtain asymmetric and non-convex estimated DoA, reducing the conservativeness. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

Geometrically, a complex dynamical network (CDN) can be regarded as the interconnected system composed of the node subsystem (NS) and the link subsystem (LS) coupled with each other. Guided by this idea, in order to achieve the goal of each node following asymptotically its own reference target in a CDN, this paper investigates the model following adaptive control (MFAC) problem of NS via the dynamics of links, which implies that the LS plays the important dynamic auxiliary role in the MFAC realization of nodes. Meanwhile, we focus on the condition that the links state information is unavailable, due to sensor practical application and measurement cost constraints. To obviate this restriction, we construct the asymptotical state observer for the LS. Next, to achieve the control goal of this paper, an appropriate Lyapunov candidate function is selected, by which the MFAC scheme for NS is synthesized based on the state observer of LS. Finally, the simulation example is performed to demonstrate the theoretical results in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a novel, five-dimensional memristor synapse-coupled Izhikevich neuron model under electromagnetic induction. Firstly, we analyze the global exponential stability of the presented system by constructing an appropriate Lyapunov function. Furthermore, the Hamilton energy functions of the model and its corresponding error system are derived by using Helmholtz's theorem. In addition, the influence of external current and system parameters on the dynamical behavior are investigated. The numerical simulation results indicate that the discharge pattern of excitatory and inhibitory neurons changes significantly when the amplitude and frequency of the external stimulus current are applied at different degrees. And the crucial dynamical behavior of the neuronal system is determined by the intensity of modulation of the induced current and the gain in the electromagnetic induction. Moreover, the amount of Hamilton energy released by the model could be evaluated during the conversion between the distinct dynamical behaviors. [ABSTRACT FROM AUTHOR]

This paper focuses on the finite-time tracking control problem of shield tunneling systems in the presence of constraints on the states and control input. By modeling the system based on the LuGre friction model, an effective method of tracking control in finite time is designed to overcome these actual constraints at the same time. First, the constraint on the system state is transformed into a symmetric constraint on the tracking error, and the constraint on control input is handled by designing an auxiliary differential equation. Then, radial basis function (RBF) neural networks are introduced to approximate the uncertainties. Next, using an adaptive finite-time backstepping method and choosing a logarithmic barrier Lyapunov function (BLF), a finite-time controller is designed to realize the finite-time stability of the closed-loop system. Finally, a simulation example is given to verify the correctness and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonautonomous viscoelastic wave equation with linear damping and delayed terms. Under some appropriate assumptions, we prove the global existence using the semigroup theory. Furthermore, for a small enough coefficient of delay, we obtained a stability result via a suitable Lyapunov function where the kernel function decays exponentially [ABSTRACT FROM AUTHOR]

This paper proposes a prescribed performance control policy for spacecraft attitude tracking control. The designed controller employs a kind of performance envelope function that can configure the convergence rate arbitrarily. Moreover, the controller design is based on the barrier Lyapunov function and indirect adaptive methods, which can suppress the fluctuation of external disturbances to obtain lower steady-state errors. Compared to prior studies on spacecraft attitude tracking, the proposed policy can arbitrarily configure the system convergence performance to achieve performance trade-offs in different scenarios. Moreover, the barrier Lyapunov function design and adaptive methods can achieve low steady-state errors with low computational resource consumption. Simulations that verify its effectiveness and superiority are provided herein. [ABSTRACT FROM AUTHOR]

This paper studies an adaptive fault tolerant control (AFTC) scheme for a continuum robot subjected to unknown actuator faults, dynamics uncertainties, unknown disturbances, and prescribed performance. Specifically, to deal with uncertainties, a function approximation technique (FAT) is employed to evaluate the unknown actuator faults and uncertain dynamics of the continuum robot. Then, a nonlinear disturbance observer (DO) is developed to estimate the unknown compounded disturbance, which contains the unknown disturbances and approximation errors of the FAT. Furthermore, the prescribed error bound is treated as a time-varying constraint, and the controller design method is based on an asymmetric barrier Lyapunov function (BLF), which is operated to strictly ensure the steady-state and transient performance of the continuum robot. Afterwards, the simulation results validate the effectiveness of the proposed AFTC in dealing with the unknown actuator faults, uncertainties, unknown disturbances, and prescribed performance. Finally, the effectiveness of the proposed AFTC scheme is verified through experiments. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust finite-time control scheme is specifically designed for a class of under-actuated nonlinear systems. The proposed scheme integrates a reaching phase-free integral backstepping method with an integral terminal fractional-order sliding mode to ensure finite-time stability at the desired equilibria. The core of the algorithm is built around proportional-integral-based nonlinear virtual control laws that are systematically designed in a backstepping manner. A fractional-order integral terminal sliding mode is introduced in the final step of the design, enhancing the robustness of the overall system. The robust nonlinear control algorithm developed in this study guarantees zero steady-state errors at each step while also providing robustness against matched uncertain disturbances. The stability of the control scheme at each step is rigorously proven using the Lyapunov candidate function to ensure theoretical soundness. To demonstrate the practicality and benefits of the proposed control strategy, simulation results are provided for two systems: a cart–pendulum system and quadcopter UAV. These simulations illustrate the effectiveness of the proposed control scheme in real-world scenarios. Additionally, the results are compared with those from the standard literature to highlight the superior performance and appealing nature of the proposed approach for underactuated nonlinear systems. This comparison underscores the advantages of the proposed method in terms of achieving robust and stable control in complex systems. [ABSTRACT FROM AUTHOR]

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]