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In this article, the issue of positive L₁ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T-S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T-S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with L₁ performance. Some solvability conditions for positive L₁ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.

This work concerns the event-based asynchronous filtering problem for T-S fuzzy nonhomogeneous Markov switching systems with variable packet dropouts. The discrete-time nonhomogeneous Markov process is adopted to depict mode switching among subsystems, in which the time-varying transition probabilities are characterized by a polytope structure. The variable packet dropouts are developed to describe the randomly occurring packet dropouts, where the arriving rate remains variable and uncertain. Aiming to save the limited network bandwidth, event-triggered strategy and quantization scheme are presented. By establishing the fuzzy-rule-dependent Lyapunov functional and applying a hidden Markov model policy, sufficient criteria are gained and asynchronous filters are designed by solving linear matrix inequalities (LMIs). Finally, the applicability of the proposed filtering strategy is verified by an inverted pendulum model.

The issue of sliding-mode control (SMC) design is studied for a class of nonlinear semi-Markovian switching systems (S-MSSs) via T-S fuzzy approach. Compared with previous literature, novel integral sliding-mode surfaces (ISMSs) are developed to depend on the designed controller gains and projection matrices. The aim of this work is to design an appropriate fuzzy SMC law under complex stochastic semi-Markovian switching process. For this purpose, the novel ISMSs are developed under the T-S fuzzy modeling framework. Then, based on the weak infinitesimal operator theory, sufficient conditions are given for stochastic stability criteria relying on the sojourn-time. Furthermore, an appropriate fuzzy SMC law is proposed to drive the state signals onto the predefined fuzzy manifold. Finally, an electric circuit model illustrates the effectiveness of the theoretical findings.

This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters. As a new attempt, the SMC strategy is considered in the study of discrete-time Markov jump SPSs. Subsequently, in order to design a sliding-mode controller to ensure the stability of the proposed system, a novel integral sliding surface is constructed, and an SMC law is synthesized to ensure the reachability of the sliding surface. Through the utilization of Lyapunov stability and SMC theory, sufficient conditions are derived to ensure the state trajectories of the system are driven to a predefined sliding surface and the closed-loop sliding mode dynamics are stochastically stable. Finally, the applicability of the proposed SMC strategy is verified by a numerical example and a practical electric circuit model.

The distributed stabilization problem is studied in this article for a group of heterogeneous second-order agents in the strong-weak competition network containing three kinds of relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. The entire network satisfies the structural balance condition which can be partitioned into two subnetworks, while the strong and weak competitions are alternate actions on the agents from different subnetworks. To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced correspondingly and several effective sufficient conditions are attained. Finally, the derived analytical results are demonstrated by performing numerical simulations.

This paper investigates H ∞ exponential synchronization (ES) of neural networks (NNs) with delay by designing an event-triggered dynamic output feedback controller (ETDOFC). The ETDOFC is flexible in practice since it is applicable to both full order and reduced order dynamic output techniques. Moreover, the event generator reduces the computational burden for the zero-order-hold (ZOH) operator and does not induce sampling delay as many existing event generators do. To obtain less conservative results, the delay-partitioning method is utilized in the Lyapunov–Krasovskii functional (LKF). Synchronization criteria formulated by linear matrix inequalities (LMIs) are established. A simple algorithm is provided to design the control gains of the ETDOFC, which overcomes the difficulty induced by different dimensions of the system parameters. One numerical example is provided to demonstrate the merits of the theoretical analysis.

This paper emphasizes on a novel fixed-time stability strategy and its application to fixed-time synchronization control for a class of semi-Markov jump delayed Cohen-Grossberg neural networks (SMJDCGNNs). First, a novel fixed-time stability strategy for a class of nonlinear delayed systems is proposed, which is a generalization of the existing stability strategies. Second, the addressed fixed-time stability strategy is applied to solving fixed-time synchronization control for a class of SMJDCGNNs, whose framework generalizes the existing Cohen-Grossberg neural networks (CGNNs). The application testifies that compared with the existing fixed-time stability strategies, the obtained fixed-time stability strategy can provide a tighter settling time which can more effectively and accurately estimate the convergence time of the studied delayed system. Finally, we give a comparative example to illustrate the validity of our results.

This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.

This article addresses the issue of input–output finite-time stability (IO-FTS) for nonlinear systems by employing sliding-mode control (SMC) methodology. Many practical systems subject to complex factors, such as the single-link robot arm model (SLRAM), can be characterized as nonlinear systems. Our attention is focused on designing a fuzzy-model-based finite-time SMC law to attenuate the influences of uncertainty, nonlinear term, and external disturbance during the finite-time region. First, a novel integral sliding-mode surface is proposed based on the Takagi–Sugeno fuzzy rule. Then, by using the key point of Lyapunov function theory, an appropriate fuzzy SMC law is designed to make sure that the signal variables can arrive at a domain within the assigned fixed-time level. Moreover, some new IO-FTS criteria are constructed for the resulting sliding dynamics over the whole finite-time level, including reaching phase and sliding motion phase. Via the SLRAM, we demonstrate the effectiveness of the proposed SMC approach.

The issue of finite-time synchronization (FTS) of discontinuous reaction-diffusion neural networks (DRDNNs) with time-varying coefficients is investigated here. First, the effects caused by discontinuous activations are handled by differential inclusion theory. Secondly, a relaxed Lyapunov function (RLF) method is introduced to design novel control algorithms, including state-feedback control and adaptive control, to achieve FTS of DRDNNs, and the upper-bound of the settling time is explicitly estimated. In this RLF method, the LF is allowed to be nonsmooth and possess an indefinite derivative.Moreover, the FTS results via generalized pinning state-feedback and generalized pinning adaptive control are presented as two corollaries. Finally, two numerical simulations are presented to substantiate the merits of the obtained results.

This article presents sufficient conditions on Finite-Time Input-to-State Stability (FTISS) of nonlinear impulsive systems, which gathers the analysis of Input-to-State stability (ISS) and finite-t...

This paper is concerned with the global synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights, where the dynamic nodes are modeled to be discontinuous, and subject to the local Hölder nonlinear growth in a neighborhood of continuous points. Firstly, an inequality with respect to variable-order fractional derivative for convex functions is proposed. On the basis of the proposed inequality, a global convergence principle in finite time for absolutely continuous functions is developed. Secondly, based on proposed convergence principle in finite time, a new sliding mode surface is presented, and an appropriate sliding mode control law is designed to drive the trajectory of the error system to the prescribed sliding mode surface in finite time and remain on it forever. In addition, on the basis of differential inclusions theory and Lur'e Postnikov-type convex Lyapunov function approach, the sufficient conditions with respect to the global stability in finite time are established in terms of linear matrix inequalities for the error system on designed sliding mode surface. Moreover, the upper bound of the settling time is explicitly evaluated. Finally, the effectiveness and correction of synchronization strategies are illustrated through two simulation experiments.

This paper considers the Internet congestion control and consensus problems of a multi-agent system composed of a congested node, some aggregation nodes and their following nodes. First, a novel multi-agent Internet congestion control system with both discrete and distributed delays is proposed. Second, the stability and Hopf bifurcation of the congested node are discussed. Subsequently, a simple error controller designed for aggregation nodes, some necessary and sufficient conditions have been established to solve the bifurcation consensus problem between aggregating nodes and the congested node. Bifurcation consensus of aggregation nodes and their following nodes are also obtained through consensus protocols which based on a novel predictive controller. So far, the bifurcation asymptotically consensus of multi-agent Internet congestion control system is achieved. It is worth noting that conditions for global stability of system can be obtained by selecting appropriate control parameters, and conclusions of global asymptotic stability consensus is given to draw conditions for avoiding network congestion in the whole system. Finally, numerical examples illustrated the correctness and validity of the main results.

This paper considers the finite-time and fixed-time synchronization problems for the delayed inertial memristive neural networks (DIMNNs) with disturbances. Different from the existing researches, the activation functions of the investigated models are permitted to be discontinuous. In light of the Filippov solution theory and Lyapunov stability theory, a unified control strategy is designed to achieve both the goals of finite-time and fixed-time synchronization for the DIMNNs. Furthermore, some finite or fixed settling times can be expressed with different control parameters. Finally, the effectiveness of the theoretical results is illustrated by some numerical simulations, and the relationships among disturbances, controllers, and dwell time are revealed as well.

In this paper, the fixed-time consensus issue of nonlinear multi-agent systems with general time-varying topologies and stochastically switching topologies is investigated. Firstly, for the case of...

This paper mainly discusses H ∞ finite-time realization for a class of uncertain Markovian jump systems (MJSs) with unmeasurable state via sliding mode control (SMC) method. A key question is how to design an appropriate SMC approach in a finite-time to reduce the effects of model switching and external interference on the overall performance of the system under consideration. First, by designing an appropriate finite-time SMC law based on a non-fragile observer, the state trajectory can reach a specified sliding surface (SSS) within given finite-time interval. Then, by means of time-partitioning strategy, finite-time boundedness (FTBs) criteria including the reaching phase and the sliding motion phase are proposed for uncertain MJSs with H ∞ performance. Second, by solving the corresponding linear matrix inequalities (LMIs), the controller gain and the observer gain are obtained. Finally, a single-link robot arm model (S-LRAM) is given to prove the effectiveness of the proposed method.

This paper develops a fully distributed self-triggered framework for achieving the second-order consensus in multiagent systems. In this framework, a fully distributed self-triggered scheme is proposed to schedule information transmission for each communication channel. Thus, the communication frequency of each channel is significantly reduced. Here, communication over different channels is independent with each other and, thus, a channel-based control protocol is further proposed. The update times of control protocol could be also lowered in this framework. Here, an iterative evaluation method is constructed to design a fully distributed self-triggered scheme without involving any global information, especially the eigenvalue information of the Laplacian matrix. In addition, by introducing several variables, some sufficient conditions for achieving the second-order consensus and average consensus are obtained, respectively, in a distributed fashion, and the Zeno behavior is successfully eliminated. Finally, a simulation example is provided to verify the theoretical analysis.

This paper is concerned with the topological structure, reachability, and stabilization for Boolean control networks (BCNs) with state constraints via event-triggered control (ETC) scheme. In the first part, the topological structure of BCNs with state constraints is studied. Under the framework of state constrain, the definitions of fixed point and cycle are first defined. A novel phenomenon is that there may exist two kinds constrained fixed points, which are, respectively, named as the livelock and deadlock ones. It is different with the traditional fixed point. Accordingly, a formula is presented to calculate the number of constrained fixed points and constrained cycles. In the second part, the constrained reachability and stabilization problem of the event-triggered controlled BCNs are investigated. Two necessary and sufficient criteria are, respectively, obtained. Furthermore, an algorithm is developed to design all feasible controllers. Finally, a reduced model of the lac operon in the Escherichia coli is shown to illustrate the efficiency of the obtained results.

This article deals with the issue of dissipative synchronization for Markov jump neural networks subject to time-varying interval delays by using the sampled-data control method. First, a new two-sided looped-functional is introduced to improve the informativeness of the formed Lyapunov–Krasovskii functional, which takes into an account the information of the entire sampling period. Compared with some traditional methods, the information between $x(t) $ and $x(t_{k+1})$ is also emphasized. On this basis, an improved inequality technique is considered valid to acquire the less conservative synchronization criterion. In the end, two numerical examples are displayed, and a comparative example powerfully demonstrates the availability and the superiority of the developed technique.

The problem of extended dissipativity performance of a high-speed train (HST) with probabilistic delays and actuator faults under resilient reliable control has been exploited in this article. An extended dissipativity index is selected to perform a unified control design procedure for the HST dynamics, which is more general than $(\mathbb {Q},\mathbb {S},\mathbb {R})$ -dissipativity index. Specifically, a sequence of random variables responding the Bernoulli distribution is exploited to govern the probabilistic time-delays. By utilizing the tighter integral inequality (TII) and reciprocally convex inequality (RCI) technique, some criteria are launched in terms of the linear matrix inequalities (LMIs). Finally, simulations show the effectiveness and applicability of the offered control law by inspecting the Japan Shinkansen HST with its experimental values, along with a comparison study also been exploited to showing the merits and generalization of the proposed control design technique.

This brief mainly studies the economic dispatch problem (EDP) in smart grid. The purpose of this problem is to minimize the total power generation cost under the conditions of balance between supply and demand and power generation capacity constraints. A distributed continuous-time solver is proposed, which only requires the sign of relative dual variable information between neighbors, which ensures the privacy of the generators. In addition, the algorithm does not require initialization and allows online changes of network topology, load, etc. It is theoretically proved that the algorithm achieve the optimal scheduling of smart grid over undirected switching graphs under certain conditions. In the presence of gradient measurement noise, the variation form of the algorithm which converges in the mean square sense is given. Finally, the simulation example illustrates the validness of the algorithm.

In this paper, the optimization of the finite-time consensus of a multiagent system is studied when the leader is disturbed by white noise. Different from the consensus problem itself, this paper is devoted to optimizing the performance of the consensus and the constructive method and martingale method are used to guarantee the effectiveness of the optimization. Another contribution is that the problem of the optimal control with the piecewise constant controller gains under a stochastic environment is solved, and the reformed dynamic principle and the reformed Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs) are proposed by using the splitting method and Feynman–Kac formula. Furthermore, since the multiagent system often runs on a high-dimensional space, a heuristic method is proposed based on the derivation of the reformed HJB PDEs and the scalar of the computational complexity of the PDEs is equivalent to that of a system of ordinary differential equations with the same dimensions when the multiagent system can be described as a piecewise linear system. Finally, the heuristic method is compared with usual filtering methods for solving engineering problems by a numerical example and it is found that the heuristic method achieves higher precision in finite time.

This paper addresses the nonstationary quantized control problem for the discrete-time Markov jump singularly perturbed systems (MJSPSs) subject to deception attacks (DAs). The control inputs are characterized by randomly occurring DAs and nonstationary quantization simultaneously, where the DAs are depicted by means of a Bernoulli distributed sequence. By applying a multi-layer structure methodology (MLSM), the nonstationary controllers are devised for MJSPSs. Meanwhile, the correlation among system mode, controller mode, and quantizer mode are portrayed via the nonstationary Markov process. Based on a mode-dependent Lyapunov functional, sufficient criteria are established such that the resulting closed-loop system (CLS) is stochastic mean square exponential ultimately bounded (SMSEUB), and the desired controller is designed. Ultimately, two simulation examples are offered to elaborate on the validity and superiority of the proposed theoretical results.

This paper focuses on the state estimation problem for a type of coupled neural networks with multiple time delays and markovian jumping communication topologies. To avoid unnecessary resources consuming, a novel state estimator is designed based on event-triggered mechanism, in which the control input of each node is only updated when the measurement output error exceeds a predefined threshold. The event-triggering time sequence is a subset of the switching time sequence, which can naturally excludes the Zeno-behavior. By utilizing an appropriate Lyapunov-Krasovskii functional, as well as the weak infinitesimal operator of Markov process and some algebraic inequalities, an easy-to-check sufficient criterion is derived to ensure the exponential ultimate boundedness of the estimation error. Finally, a simulation example is presented to illustrate the applications and effectiveness of the theoretical results.

In this paper, we focus on the global exponential cluster synchronization of switched fractional-order complex dynamical networks (FCDNs) with switching topology and impulses, where the impulse effects are independent or dependent of switched modal. Compared with the literature, impulsive effects can occur not at the mode switched moment, but also at the instants without me AII) with the average dwell time (ADT) and the mode-dependent average impulsive interval (MDAII) with the mode-dependent average dwell time, by adopting multiple Lyapunov functional approach, the inequality analysis technique and pinning control strategy, the global exponential cluster synchronization conditions are achieved. Finally, the validity of theoretical results is verified by two simulation examples.

This paper concerns a positive $\mathcal {L}_{1}$ observer for positive nonlinear semi-Markovian switching systems (MSSs) via the expansion of Taylor formula and the fuzzy Lyapunov function approach, in which semi-Markovian switching parameters, positivity, Takagi–Sugeno (T–S) fuzzy, and external disturbance are all considered in a unified framework. A fuzzy Lyapunov function approach with less conservativeness is introduced into the research of positive systems. In the system under consideration, positive S-MSSs with the semi-Markovian process can describe more complex systems in a practical control process. The main motivation of this paper is that the practical system subject to positivity and abrupt changes can be described by positive nonlinear S-MSSs, which always needs to consider the external disturbance. First, by using the normalized membership function approach, positive nonlinear S-MSSs can be represented by local positive T–S fuzzy S-MSSs. Second, by constructing the fuzzy Lyapunov function, some sufficient conditions are proposed for stochastic stability and $\mathcal {L}_{1}$ -gain performance analysis, respectively. Then, a positive $\mathcal {L}_{1}$ observer in a novel standard linear programming condition is designed to guarantee the resulting closed–loop augmented system is positive and stochastically stable with a required $\mathcal {L}_{1}$ -gain performance. Finally, a practical example about the epidemiological model is introduced to show the effectiveness of the main theory.

This work is devoted to investigating the asynchronous quantized control of discrete-time Markovian switching Lur’e systems with an event-triggered mechanism. To model the asynchronous controller and the quantization effects, the hidden Markov model is employed. For reducing the burden of communication bandwidth, an event-triggered mechanism is adopted. By choosing the proper stochastic Lyapunov functional, sufficient conditions are derived. Finally, a practical example is given to illustrate the effectiveness and efficiency of the proposed method.

This brief studies the synchronization problem for a class of QUAD and interconnected nonlinear multi-agent systems (MASs). A dynamic event-based control scheme is designed, and two event-based synchronization conditions are constructed by utilizing stability theory. Moreover, the Zeno-behavior can be excluded in the MASs. An example and its simulation are given to verify the applicability of the designed dynamic event-based protocol for MASs.

In this paper, the global Mittag-Leffler consensus tracking issue is considered for fractional singularly perturbed multi-agent systems (FSPMASs) based on event-triggered control strategy, where the inherent dynamic is modeled to be a discontinuous function with nondecreasing property. Firstly, a differential inequality with respect to fractional-order derivative of convex function is developed. As the special cases, the inequalities about fractional-order derivative of three known functions are also addressed. Secondly, a distributed event-triggered control scheme is designed to guarantee that the considered FSPMASs can achieve the global Mittag-Leffler consensus. Moreover, the Mittag-Leffer convergence speed of tracking the leader for followers can be adjusted to any desired values in advance. In addition, under fractional Filippov differential inclusion framework, by applying Lur’e Postnikov-type Lyapunov functional with variable upper limit integral item and Clarke’s non-smooth analysis technique, the global Mittag-Leffler consensus conditions are addressed in terms of matrix inequalities (MIs). Finally, two numerical simulations are provided to illustrate the validity of the proposed design method and theoretical results.

This paper studies quasi-synchronization in networked heterogeneous harmonic oscillators. By introducing a leader, two distributed synchronization protocols are first proposed for heterogeneous networks by utilizing continuous real-time information and aperiodic sampled-data information. Then, the sufficient conditions on quasi-synchronization are established for heterogeneous networks coupled with nonidentical harmonic oscillators. It is found that each follower oscillator can converge to a bounded region of the leader by adopting either a continuous-time protocol or sampled-data protocol. The upper bound of the region is solved for networked heterogeneous harmonic oscillators. Finally, an electrical network is provided to illustrate the applicability of the theoretical results, and two examples are provided to illustrate the effectiveness of the sufficient criteria.

This paper discusses the problem of bifurcations for a delayed fractional-order neural networks (FONNs) with multiple neurons. Self-connection delay is carefully viewed as a bifurcation parameter, stability zones and bifurcation conditions are nicely established, respectively. It declares that self-connection delay immensely affects the stability and bifurcation of the developed FONNs. The explored FONNs illustrate preferable stability performance if selecting a lesser self-connection delay, and Hopf bifurcation generates once they overstep the critical values. Moreover, the effects of fractional order on the bifurcation points are fully studied. It detects that the emergence of bifurcation can be lagged as fractional order amplifies. The verification of the feasibility of the developed theory is implemented via numerical experiments.

We provide feasible criteria for stabilization of stochastic differential equations driven by $G$-Brownian motion based on discrete-time observations. We extend the results in Ren, Yin, and Sakthiv...

This paper considers the prespecified-time synchronization issue of switched coupled neural networks (SCNNs) under some smooth controllers. Different from the traditional finite-time synchronization (FTS), the synchronization time obtained in this paper is independent of control gains, initial values or network topology, which can be pre-set as to the task requirements. Moreover, unlike the existing nonsmooth or even discontinuous FTS control strategies, the new proposed control protocols are fully smooth, which abandon the common fractional power feedbacks or signum functions. Finally, two illustrative examples are provided to illustrate the effectiveness of the theoretical results.

This paper investigates the finite-time synchronization issue for semi-Markov jump inertial neural networks, in which the sampled-data control is employed to alleviate the burden of the limited communication bandwidth. Due to the existence of inertial item, the semi-Markov jump inertial neural networks as hybrid neural systems, are depicted with second-order derivatives for the first time, which can be turned to first-order derivatives by the variable transformation. Furthermore, by applying appropriate integral inequalities and constructing the proper Lyapunov functional, some sufficient conditions, which not only guarantee the finite-time synchronization of the resulting error system but also ensure a specified level of $\mathcal {L}_{2}$ - $\mathcal {L}_{\infty }$ performance, are acquired based on the optimization of integral inequality technique. A numerical example is, eventually, proposed to substantiate the validity of the developed method.

There are few results concerning consensus of multiagent systems (MASs) based on partial differential equations (PDEs), and the problem of how to act boundary control based on distributed measurement on spatial boundary points of MASs has not been solved. This paper addresses boundary control based on distributed measurement for output consensus of leader-following directed MASs modeled by parabolic PDEs. First, a boundary controller acting on spatial boundary points is designed by considering the delivered information produced by agents communicating with neighborhoods. Without considering input constraint, the Lyapunov’s direct method is used to obtain a sufficient condition on the existence of the boundary controller to achieve output consensus. The condition is expressed as a form of the feasibility of LMIs. After that, the whole input constraint for MASs is given. And then, one more condition on control gains is obtained to ensure the existence of the boundary controller with input constraint. Finally, one numerical example with two cases illustrates the theoretical analysis results.

Based on previous research on the finite-time output synchronization of coupled neural networks (CNNs), this paper proposes the novel concept of fixed-time output synchronization and fixed-time $H_{\infty }$ output synchronization, and extends the corresponding results to coupled reaction-diffusion neural networks (CRDNNs). In addition, the output delayed coupling and discontinuous activations are taken into consideration. Then, two types of CRDNNs are considered, the CRDNNs with external disturbances or that without disturbances. With the Lyapunov functional and fixed-time control theory, a novel feedback control scheme is proposed to guarantee fixed-time output synchronization and $H_{\infty }$ output synchronization of the considered CRDNNs respectively. Finally, numerical examples are given to demonstrate the correctness of our results.

This work focuses on exponential synchronization for a class of partially coupled heterogeneous networks with time-delays and heterogeneous impulses. The synchronization targets are selected as the common equilibrium solution and the average trajectory, respectively. Some synchronization criteria are deduced by using Lyapunov function and comparison principle.

In this article, finite-time and fixed-time synchronizations (FFTS) of fuzzy cellular neural networks (FCNNs) with interaction and proportional delay terms have been investigated. The synchronizations of FCNNs are achieved with the help of p-norm based on the inequalities defined in Lemmas 2.1 and 2.2. The analysis of the method with some useful criteria is also used during the study of FFTS. Under the Lyapunov stability theory, FFTS of fuzzy-based CNNs with interaction and proportional delay terms can be achieved using controllers. Moreover, the upper bound of the settling time of FFTS is obtained. In view of settling points, the theoretical results on the considered neural network models of this article are more general as compared to the fixed time synchronization (FTS). The effectiveness and reliability of the theoretical results are shown through two numerical examples for different particular cases.

A neural-network model of fractional order with impulsive perturbations, time-varying delays, and reaction-diffusion terms is investigated in this article. The focus is on investigating qualitative properties of the states and developing new almost periodicity and stability criteria. The uncertain case is also considered. Examples are established and the effectiveness of the obtained criteria is demonstrated. © 2013 IEEE.

This article investigates the set stabilization of impulsive Boolean control networks (IBCNs) by sampled-data state feedback control based on a hybrid index model. It is worth mentioning that the 2-D index model has the ability to characterize the instantaneousness of ideal impulses and describe complicated impulsive behaviors. To avoid Zeno phenomenon, the judging conditions for forward completeness are derived. Subsequently, an algorithm is designed to obtain the largest sampled point control invariant set (SPCIS) of a given set in the hybrid domain, and its validity is further authenticated. Accordingly, a necessary and sufficient condition is derived for the set stabilization of IBCNs in the hybrid domain, and all time-optimal sampled-data state feedback controllers are designed. The similar results are also obtained for IBCNs in the time domain. Compared with set stabilization in the time domain, set stabilization in the hybrid domain not only focuses on the dynamics at each time instant but also concerns every jumping state. It results in that every SPCIS in the hybrid domain is a subset of a certain SPCIS in the time domain. Eventually, the $\lambda$ switch with impulsive disturbances is modeled as a reduced IBCN, which is presented to demonstrate the obtained results.

In this paper, a class of discrete-time singularly perturbed switched systems $\left ({\text {SPSSs}}\right) $ with persistent dwell-time $\left ({\text {PDT}}\right)$ switching law is firstly proposed. Using the slow-state feedback control method, sufficient conditions to ensure the global uniform exponential stability of the closed-loop PDT SPSSs are derived. Based on the aforementioned conditions, the analyses of the extended dissipative performance of the closed-loop PDT SPSSs and a preferable decoupling method deriving the mode-dependent controller gains are given for the first time. Finally, the potential practicability of the method is verified by a purely numerical example and a tunnel diode circuit model, and a convex optimization method calculating the upper bound of the singular perturbation parameter is provided.

For Markov switched stochastic functional differential systems (SFDSs), asymptotic property is one of the most desired issues. Recently, a new class of delay-dependent asymptotic stability for non-linear Markov switched SFDSs was investigated. However, the existing references do not take the convergent speed and non-autonomous factor into consideration. Therefore, by means of multiple Lyapunov–Krasovskii functionals, this study is devoted to examine the exponential stability for highly non-linear autonomous Markov switched SFDSs and the exponential stability, polynomial stability and polynomial growth at most for highly non-linear non-autonomous systems, where all the criteria rely on the intervals lengths of continuous delays. In addition, the properties of boundedness and asymptotic stability are as well explored.

This paper expatiates the stability and bifurcation for a fractional-order neural network (FONN) with double leakage delays. Firstly, the characteristic equation of the developed FONN is circumspectly researched by employing inequable delays as bifurcation parameters. Simultaneously the bifurcation criteria are correspondingly extrapolated. Then, unequal delays-spurred-bifurcation diagrams are primarily delineated to confirm the precision and correctness for the values of bifurcation points. Furthermore, it lavishly illustrates from the evidence that the stability performance of the proposed FONN can be demolished with the presence of leakage delays in accordance with comparative studies. Eventually, two numerical examples are exploited to underpin the feasibility of the developed theory. The results derived in this paper have perfected the retrievable outcomes on bifurcations of FONNs embodying unique leakage delay, which can nicely serve a benchmark deliberation and provide a comparatively credible guidance for the influence of multiple leakage delays on bifurcations of FONNs.

In this paper, a continuous-time multiagent system is proposed for solving optimal resource allocation problems with local allocation feasible constraints. In the system, all the primal agents are divided into different groups. We use dual variables which describe the dual agents to represent the groups of the original agents. The groups of dual agents are used to communicate with others on behalf of the primal agents to reduce communication costs. That is to say, primal agents aim to seek their own optimal solutions by using local information. And dual agents represent primal agents to communicate with other agents in different groups by using the whole group information. The two kinds of agents cooperate to find the optimal solution of the problem. In this way, we only need to know the connections of dual agents to design the multiagent network, and do not need to consider the connections of the primal agents. So the communication cost and the amount of variables will be largely reduced especially for large-scale problem. Furthermore, it is proved that the multiagent system can reach consensus with respect to the dual variables. At the same time, the primal variables are convergent to the optimal solutions of the optimization problem under some certain assumptions on the communication network. For large-scale problem if we take the groups as areas, then the system is suitable for multiarea problem. Simulation results are presented to demonstrate the performance of the proposed multiagent system.

The work presented in this paper concerns a switching-based control formulation for multi-intersection and multiphase traffic light systems. A macroscopic traffic flow modeling approach is first presented, which is instrumental to the development of a model-based and switching-based optimization method for traffic signal operation, in the framework of adaptive dynamic programming (ADP). The main advantage of the switching-based formulation is its capability to determine both 'when' to switch and 'which' mode to switch on without the need to use the cycle-based average flow approximation typical of state-of-the-art formulations. In addition, the framework can handle different cycle times across intersections without the need for synchronization constraints and, moreover, minimum dwell-time constraints can be directly enforced to comply with minimum green/red times in each phase. The simulation experiments on a multi-intersection and multiphase traffic light systems are presented to show the effectiveness of the method.

We propose Lyapunov functions for the set stability of Boolean networks (BNs) and control Lyapunov functions for the feedback set stabilization and the synchronization of Boolean control networks (BCNs) in this brief. Meanwhile, some propositions of these Lyapunov functions are put forward. Sufficient and necessary conditions for the set stability of BNs, the feedback set stabilization of BCNs and the synchronization of drive-response coupled BCNs in the form of Lyapunov functions are presented successively. Moreover, an algorithm is given to construct control Lyapunov functions and state feedback controllers simultaneously for the synchronization of coupled BCNs. Two examples are given to illustrate the obtained results.

The present draft investigates the finite-time stabilization of T–S fuzzy semi-Markov switching systems by using a coupling memory sampled-data control approach. The main study concerned is how to effectively design the sampled-data control such that closed-loop T–S fuzzy semi-Markov switching systems is finite-time boundedness. By utilizing a Bernoulli distributed sequence, a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived. By virtue of fuzzy-basis-dependent membership functions, an asynchronous approach is proposed for T–S fuzzy semi-Markov switching system. Moreover, the inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies.

This paper is concerned with the synchronization of stochastic delayed multilayer networks with additive couplings. Multilayer networks are a kind of complex networks with different layers, which consist of different kinds of interactions or multiple subnetworks. Additive couplings are designed to capture the different layered connections. Based on additive couplings, several sufficient conditions are obtained to guarantee the synchronization of chaotic stochastic delayed coupled multilayer network. More specifically, on one hand, we obtain some sufficient conditions to guarantee that the stochastic multilayer network can be synchronized almost surely without control input. On the other hand, we propose three synchronization schemes by designing controllers. Scheme I: It is assumed that only a part of the nodes are allowed to be controlled directly. Scheme II: Control all nodes of the complex system by using only one controller. Scheme III: Pinning adaptive controller. Finally, an example and its simulations are given to show the effectiveness of our control schemes.

The issue of resilient reliable dissipativity performance index for systems including actuator faults and probabilistic time-delay signals via sampled-data control approach is investigated. Specifically, random variables governed by the Bernoulli distribution are examined in detail for the random time-delay signals. By using the Lyapunov–Krasovskii functionals together with the Wirtinger double integral inequality approach and reciprocally convex combination technique, which reflects complete information on the certain random sampling; as a result, a new set of sufficient criterion is launched to ensure that the proposed closed-loop system is strictly ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ - ${\gamma }$ -dissipative. The proposed criterion for dissipativity-based resilient reliable controller is expressed in the form of linear matrix inequalities. The major contributions of this paper is ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ - ${\gamma }$ -dissipativity concept can be adopted to analyze more dynamical performances simultaneously, such as ${\mathcal {H}_\infty }$ , passivity, mixed ${\mathcal {H}_\infty }$ , and passivity performance for the proposed system model by choosing the weighting matrices ${(\mathbb {Q},\mathbb {S},\mathbb {R})}$ . Finally, an interesting simulation example is demonstrated to showing the applicability and effectiveness of the theoretical results together with proposed control law by taking the experimental values of the high-incidence research model and rotary servo system.

In this article, we investigate the Lyapunov stability problem for impulsive systems via event-triggered impulsive control, where dynamical systems evolve according to continuous-time equations most of the time, but occasionally exhibit instantaneous jumps when impulsive events are triggered. We provide some Lyapunov-based sufficient conditions for uniform stability and globally asymptotical stability. Unlike normal time-triggered impulsive control, event-triggered impulsive control is triggered only when an event occurs. Thus our stability conditions rely greatly on the event-triggering mechanism given in terms of Lyapunov functions. Moreover, the Zeno behavior can be excluded in our results. Then, we apply the theoretical results to the nonlinear impulsive control system, where event-triggered impulsive control strategies are designed to achieve stability of the addressed system. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the proposed results.