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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]

In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented. [ABSTRACT FROM AUTHOR]

In view of the problem that time delay always existing in wide area power system can cause severe effects on the operation performance of the whole system, this paper studies the stability of the wide area power system with interval time-varying delays. Firstly, the model of wide area power system with interval time-varying delay is established, based on that, a new augmented vector and new Lyapunov-Krasoskii functional (LKF) are constructed. Then, the delay-partitioning approach, Wirtinger integral inequality, free-matrix-based inequality and convex combination approach are used to estimate the derivative of the functional, and as a result, a less conservative stability criterion for the delayed power system is obtained. Finally, numerical simulations of the typical second-order system, the single machine system and two-area four-generator power system are given to illustrate that the proposed method in this paper expands the stability margin of the system effectively. [ABSTRACT FROM AUTHOR]

In this paper, neutral type shunting inhibitory cellular neural networks withDoperator are considered. Based on Lyapunov functional method and differential inequality technique, some new criteria are derived to guarantee the existence and global exponential stability of pseudo almost periodic solutions of considered systems. In addition, an example and its numerical simulations are provided to show the validity and the advantages of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the salient features of a stochastic multigroup SEI epidemic model. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distribution indicates that the diseases will be prevalent and persistent in the long term. In addition, we make up adequate conditions for complete eradication and wiping out of the diseases. Some numerical simulations are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a stochastic multigroup S-DI-A model for the transmission of HIV with general incidence rate. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a proper stochastic Lyapunov function. The stationary distribution implies that the diseases will be persistent in the long term. Some numerical simulations are introduced to illustrate our theoretical result. [ABSTRACT FROM AUTHOR]

This paper addresses the trajectory tracking control problem of a planar vertical take-off and landing (PVTOL) aircraft in the presence of position constraints and external disturbances. A novel robust constrained control approach is proposed by incorporating the barrier Lyapunov function (BLF) and nonlinear damping items within the framework of dynamic surface control design. The dynamic surface control is used to avoid the 'explosion of terms' problem of the traditional backstepping control. The tan-type BLF is utilised to preserve the position tracking errors always within the predefined position constraints. The nonlinear damping items are applied to handle the effect of external disturbances. The uniform ultimate boundedness of the resulting closed-loop system is rigorously proved through the Lyapunov's direct method. A distinct feature of the proposed control approach is that it is a general methodology for the trajectory tracking control of PVTOL aircraft with or without position constraints. Both theoretical analysis and numerical simulations illustrate the effectiveness and benefits of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, exponential finite-time coordination problems of multi-agent systems are investigated, including containment control and consensus. The theoretical basis is that a class of nonlinear systems has favourable finite-time convergence characteristic. For the objective of containment control, the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time. For the objective of consensus, a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time. The distinguished features of this paper lie in the following two points: (1) a smaller settling time of the Lyapunov function is obtained, which manifests in a faster convergence rate than the traditional one and (2) the weakly connected topology considered in this paper is more general than the ones (a spanning tree, a spanning forest, and so on) in other coordination problems. All the results are illustrated by some simulations. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time coupled within-host and between-host epidemic model with environmentally driven and saturation incidence is discussed. The model is divided into an isolated fast model and an isolated coupled slow time model by using the way of limit equations. The positivity, boundedness and existence of equilibria for isolated fast and coupled slow time models are investigated, respectively. The global stability of infectious-free and infectious equilibria for the isolated fast time model is established by means of the Lyapunov functions and LaSalle's invariance principle. The local asymptotic stability of disease-free and endemic equilibria for the coupled slow time model is obtained by using the linearization method. When there are two positive equilibria in the coupled slow time model, the existence of backward bifurcation also is established. Furthermore, the correctness of theoretical conclusions and the rationality of conjecture are verified by the numerical simulations. [ABSTRACT FROM AUTHOR]

This paper discusses the design problem of distributedH∞Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with anH∞performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimalH∞observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method. [ABSTRACT FROM PUBLISHER]

In this paper, an event-triggering scheme is implemented in uncertain switched linear systems with time-varying delays and exogenous disturbance. Instead of standard periodically time-triggered, sampled-data control systems, the event-triggered control systems sample data only when an event, typically defined as some performance error exceeding a tolerant bound, occurs. Specifically, considering the disturbance existing in the system, the event-triggered robustH∞control problem is studied. In order to guarantee the robustH∞performance, the event-triggered full state feedback control, multiple Lyapunov functions method and state-dependent switching law are utilised to construct sufficient conditions in terms of linear matrix inequalities. In particular, since the event-triggered signals and switching signals may interlace with each other, the influence from them on the analysis of robustH∞performance is clarified. Subsequently, sufficient design conditions of the sub-controllers’ gains are further presented. Moreover, the Zeno problem is discussed to exclude continuously triggering and sampling. Finally, numerical simulations are provided to verify the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is considered to be about the existence of periodic solutions for neutral coupled oscillators networkwith feedback control and time-varying delay (NCONFT). Based on the systematic method which is firstly applied for NCONFT and consisting of coincidence degree theory, graph theory, and Lyapunov method, some sufficient criteria are obtained to verify the existence of periodic solutions for NCONFT. What's more, how coupling topology, feedback control, and time-varying delay affect the existence of periodic solutions for NCONFT can be shown by these sufficient criteria. Finally, a numerical simulation is offered to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The paper investigates the distributed convex optimisation problem of multi-agent systems over strongly connected and balanced digraph with time delay. To reduce the traffic among agents and the control inputs' update frequency, a sample-based distributed event-triggered zero-gradient-sum optimisation algorithm has been proposed. A sufficient stability condition with respect to the related parameters and time delay is derived via the Lyapunov function approach. Moreover, it is proved that the states of agents asymptotically converge to the global optimal point. Since the sampling control is adopted, Zeno behaviour can be naturally excluded. The results of the numerical simulation illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with boundary output feedback stabilisation of two parallel coupled string equations with matched external disturbance. By the method proposed by Feng and Guo in IEEE Transactions on Automatic Control [62(2017), pp. 3774–3787], we design a disturbance estimator first which is used to cancel the effect of disturbance in the feedback loop. The other part of output feedback controller is designed to make system stable. Then operator semigroup and Lyapunov function methods are adopted to prove that the closed-loop system admits a unique solution in state space, the solution of original system is asymptotically stable and one of the disturbance estimator system is bounded. Finally, numerical simulations are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we propose a sampled-data control law in the stabilisation problem of nonstationary motion of nonholonomic mobile robot. We assume that the robot moves on a horizontal surface without slipping. The dynamical model of a mobile robot is considered. The robot has one front free wheel and two rear wheels which are controlled by two independent electric motors. We assume that the controls are piecewise constant signals. Controller design relies on the backstepping procedure with the use of Lyapunov vector-function method. Theoretical considerations are verified by numerical simulation. [ABSTRACT FROM PUBLISHER]

This paper introduces an adaptive fractional-order sliding-mode controller for stabilization of a two-axis gimbal platform in the presence of the torque disturbance effects. To tend the angular velocities of the inner gimbal in the elevation and azimuth axes to zero, an adaptive fractional-order sliding-mode approach is utilized. To achieve this goal, fractional-order sliding surfaces in both azimuth and elevation axes and the corresponding adaptive controllers with adjustable parameters tuned according to Lyapunov-based adaptation mechanisms are employed. The optimal value of the fractional order is obtained through an integral square error performance index minimization. The moments products uncertainties are incorporated in the design procedure. The numerical simulations demonstrate that the proposed control approach is robust against the moments products variations. [ABSTRACT FROM AUTHOR]

The problem of stabilisation of a class of nonlinear continuous-time systems with asymmetric saturations on the control is studied in this paper. By combining the parametric Lyapunov equation approach and gain scheduling technique, a state feedback gain scheduling controller is proposed to solve the stabilisation problem of systems with unsymmetrical saturated control. The proposed gain scheduled approach is to increase the value of the design parameter so that the convergence rate of the closed-loop system can be increased. Numerical simulations show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered H ∞ control problem for networked switched systems with a mixed time and state-dependent switching law. By the event-triggering strategies, only necessary samplings of feedback signals are determined to be released. The advantages are that redundant transmissions and updates can be reduced. By the adopted switching law, each sub-system will work for a minimum dwell time, and then a state-dependent switching starts to work. Specifically, by using discrete event-triggering strategies and considering the effects of transmission delays, a time-delay closed-loop switched system is first established. Then, by utilising multiple Lyapunov functions method, sufficient conditions are presented to ensure the stability of the closed-loop switched system with a certain H ∞ performance level. In particular, since the switching instants and the event-triggered instants may be coupled, typical cases are discussed in detail. Moreover, the co-design conditions for state-feedback sub-controller gains and event-triggering parameters are developed. Finally, the effectiveness of the proposed method is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies a class of inertial neural networks involving proportional delays. Without adopting reduced order method, by combining Lyapunov function method with differential inequality approach, some novel assertions are gained to validate the global generalised exponential stability of the addressed model, which are new and complement some previous works. In the end, some examples with their numerical simulations are carried out to substantiate the correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper considers the fault detection problem over finite-frequency domain for a class of discrete time-delayed networked systems subject to round-robin protocol. This protocol is a periodic one to schedule the information transmitted via a shared communication network with an intent to prevent the data from collisions. In this scenario, the error dynamics can be regarded as a periodic protocol-induced system. The aim of the problem addressed is to design a fault detection filter that (1) the sensitivity of the residual to the fault is enhanced by means of a maximised H − index and (2) the effect from the exogenous disturbances on the residual is decreased with considering a minimised H ∞ index. By resorting to a Lyapunov function, an improved version of generalised Kalman–Yakubovich–Popov lemma (GKYP) is first developed for protocol-induced periodic system. Then, in light of such a lemma, sufficient conditions are derived to guarantee both the fault sensitivity and the disturbance attenuation capability by solving a set of matrix inequalities. Finally, the usefulness of the presented fault detection algorithm is utilised via a numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses a robustH∞fuzzy observer-based tracking design problem for uncertain Takagi–Sugeno fuzzy systems with external disturbances. To have a practical observer-based controller, the premise variables of the system are assumed to be not measurable in general, which leads to a more complex design process. The tracker is synthesised based on a fuzzy Lyapunov function approach and non-parallel distributed compensation (non-PDC) scheme. Using the descriptor redundancy approach, the robust stability conditions are derived in the form of strict linear matrix inequalities (LMIs) even in the presence of uncertainties in the system, input, and output matrices simultaneously. Numerical simulations are provided to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the positive invariant sets and global exponential attractive sets for a class of bidirectional associative memory (BAM)-type Cohen–Grossberg neural networks with multiple time-varying delays. By applying inequality techniques, some easily verifiable delay-independent criteria for the ultimate boundedness and global exponential attractive sets of BAM-type Cohen–Grossberg neural networks are obtained by constructing appropriate Lyapunov functions. Finally, one example with numerical simulations is given to illustrate the results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the enclosing control problem of second-order multi-agent systems is considered, where the targets can be either stationary or moving. The objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets. In order to do so, we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets. We then construct the estimator of the centre of the targets, which is used to build the control protocol to achieve equidistant circular enclosing. Using a Lyapunov function and Lasalle’s Invariance Principle, the convergency of the estimator and control protocol are, respectively, established. We then construct a smooth function to approximate the discontinuous term in the estimator. Finally, the simulations for stationary targets and moving targets are given to verify the validity of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability analysis of latent Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modelled by a general nonlinear function which satisfies a set of conditions. The model is incorporated by intracellular discrete or distributed time delays. Using the method of Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a within-host HIV-1 infection model with virus-to-cell and direct cell-to-cell transmission and explicit age-since-infection structure for infected cells is investigated. It is shown that the model demonstrates a global threshold dynamics, fully described by the basic reproduction number. By analysing the corresponding characteristic equations, the local stability of an infection-free steady state and a chronic-infection steady state of the model is established. By using the persistence theory in infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is shown that if the basic reproduction number is less than unity, the infection-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the chronic-infection steady state is globally asymptotically stable. Numerical simulations are carried out to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the design of projection-based Adaptive Sliding Mode Controller (ASMC) is presented for position control of Permanent Magnet Linear Synchronous Motor (PMLSM) with unknown mover mass. The PMLSM model was first established and a vector control based on field orientation is used to decouple the cross-coupling in motor model. ASMC has been adopted to deal with the unknown mover mass and to give robust operation against external load thrust. Based on the Lyapunov method, the stability of adaptive sliding mode-controlled PMLSM has been proven and the adaptive law has been developed. Additionally, a continuous projection operator is applied to adaptive law such as to enforce the estimated mover mass within a pre-specified bound. The performance of ASMC based on continuous projection operator is investigated via simulation results within MATLAB environment. Also, a comparison study in ASMC performance is made due to the inclusion continuous and discontinuous projection operators. The simulated results showed that ASMC based on continuous projection gives better performance than that based on discontinuous one. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov–Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerical simulation examples are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the attitude coordinated tracking control for a group of rigid spacecraft under directed communication topology, in which inertia uncertainties, external disturbances, input saturation and constant time-delays between the formation members are handled. Initially, the nominal system with communication delays is studied. A delay-dependent controller is proposed by using Lyapunov–Krasovskii function and sufficient condition for system stability is derived. Then, an integral sliding manifold is designed and adaptive control approach is employed to deal with the total perturbation. Meanwhile, the boundary layer method is introduced to alleviate the unexpected chattering as system trajectories cross the switching surface. Finally, numerical simulation results are presented to validate the effectiveness and robustness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

A novel integrated guidance and control scheme is derived for STT missile with strict constraints as desired impact angle, input saturation and partial system state in three-dimensional space. The backstepping technique and command filter are adopted for achieving input constraints, and the improved compensation signals are constructed to correct tracking errors. The integral barrier Lyapunov function is introduced to prevent the partial system states from exceeding a predefined interval. A modified extended state observer is employed to strengthen the robustness of the system further. Theoretically, the required properties of a closed-form system are proved by Lyapunov theory in detail. Numerical simulations are conducted to exhibit the performance and robustness of the IGC scheme fully. [ABSTRACT FROM AUTHOR]

The leader–follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem of leader-following multi-agent systems with fractional-order nonlinear dynamics. A typical event is defined as some error signals exceeding a given threshold. By applying Lyapunov functional approach and skills of computing function limit, consensus of the controlled multi-agent systems can be reached asymptotically. Meanwhile, the event-triggered algorithm can exclude Zeno behaviours. Finally, a numerical simulation is exploited to verify the effectiveness of the theoretical result. [ABSTRACT FROM PUBLISHER]

This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, a Lyapunov-based control concept is presented that combines variable structure and adaptive control. The considered system class consists of nonlinear single input systems which are affected by matched structured and unstructured uncertainties. Resorting to the certainty equivalence principle, the controller exploits advantages of both the sliding-mode and the adaptive control methodology. It is demonstrated that the gains of the discontinuous control action may be reduced remarkably when compared with pure sliding-mode-based approaches. The efficiency of the presented concept is demonstrated in detail, using results of numerical simulations. [ABSTRACT FROM AUTHOR]

The presence of measurement noise in the event-based systems can lower system efficiency both in terms of data exchange rate and performance. In this paper, an integral-based event triggering control system is proposed for LTI systems with stochastic measurement noise. We show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller, and also improves output performance. Using a Lyapunov approach, stability in the mean square sense is proved. A simulated example illustrates the properties of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems. [ABSTRACT FROM PUBLISHER]

This paper deals with the global property of a drinking model with public health educational campaigns. With the help of Lyapunov function, global stability of equilibria of the model is derived. The alcohol-free equilibrium is globally asymptotically stable and the alcohol problems are eliminated from population if R0 ≤ 1. A unique alcohol present equilibrium is globally asymptotically stable if R0 > 1. Furthermore, the basic reproductive R0 for the model is compared with the basic reproductive number R1 for the absence of public health educational campaigns. We conclude that the public health educational campaigns of drinking individuals can slow down the drinking dynamics. Some numerical simulations are also given to explain our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington–DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction numberand the humoral immune response activation numberwhich completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if, then the infection-free equilibrium is globally asymptotically stable (GAS), if, then the chronic-infection equilibrium without humoral immune response is GAS, and if, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we study the saturation control problem for linear time-invariant (LTI) systems subject to asymmetric actuator saturation under a switching control framework. The LTI plant with asymmetric saturation is first transformed to an equivalent switched linear model with each subsystem subject to symmetric actuator saturation, based on which a dwell-time switching controller augmented with a controller state reset is then developed by using multiple Lyapunov functions. The controller synthesis conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently. Simulation results are also included to illustrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates behaviors of three dimensional, full-scale flows generated by the newly developed INVENT HyperClassic® mixers in a primary influent channel of a wastewater treatment plant in the New York City. The ANSYS FLUENT, in conjunction with the standard k-ε turbulence closure and a multiple reference frame model, is employed for the investigations. Numerical simulations reveal large-scale circulations on cross sections perpendicular to the channel direction as a main feature of the flows, and such circulations are expected to be a key mechanism to enhance their mixing and keep solid particles in suspension. Stronger turbulence mixing in terms of turbulence kinetic energy and dissipation rate and more intensive mixing in the sense of time average and evaluated by the Lyapunov exponent are observed in the presence of two mixers than those with a single mixer. Additionally, a larger inlet velocity of the channel results in an increase in turbulence kinetic energy and dissipation rate but not necessarily a growth of the Lyapunov exponent. [ABSTRACT FROM AUTHOR]

This article explores a delayed stochastic epidemic model with double epidemic hypothesis and saturated incidence. First, we give some preliminaries of the epidemic system. Second, by building Lyapunov functions and utilizing inequalities, we study the asymptotic properties of the delayed stochastic system around each equilibrium point. Furthermore, we prove the persistence in mean of the epidemic system. In the end, several numerical simulations are presented to show that stochastic disturbance and time delay can impact the dynamics of the epidemic system. [ABSTRACT FROM AUTHOR]

In this manuscript, inertial neural networks with both time- varying and distributed delays are studied. Applying inequality techniques and Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of periodic solutions for the addressed networks is presented. The obtained results supplement some earlier publications that deal with the periodic solutions of inertial neural networks with time- varying delays. Computer simulations are displayed to check the derived analytical results. [ABSTRACT FROM AUTHOR]

The robust resilient control problem is addressed for a class of impulsive switched systems under asynchronous switching. Through constructing the piecewise Lyapunov function, a robust resilient controller is designed initially, which, for all admissible uncertainties, guarantees that the corresponding closed-loop system is exponentially stable under asynchronous switching signals. Here, the average dwell time method is utilized and the estimate of the trajectory is also presented. For the convenience of computation, all conditions are cast into the form of linear matrix inequalities. Finally, numerical examples and simulation results are demonstrated to illustrate the correctness and effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

This article studies the asymptotic behavior of a stochastic Chemostat model with Lotka–Volterra food chain in which the dilution rate was influenced by white noise. The long-time behavior of the model is studied. Using Lyapunov function and Itô's formula, we show that there is a unique positive solution to the system. Moreover, the sufficient conditions for some population dynamical properties including the boundedness in mean and the stochastically asymptotic stability of the washout equilibrium were obtained. Furthermore, we show how the solutions spiral around the predator-free equilibrium and the positive equilibrium of deterministic system. Besides, the existence of the stationary distribution is proved for the considered model. Numerical simulations are introduced finally to support the obtained results. [ABSTRACT FROM AUTHOR]

Considering interconnections among subsystems, we propose an adaptive neural tracking control scheme for a class of multiple-input-multiple-output (MIMO) non-affine pure-feedback time-delay nonlinear systems with input saturation. Neural networks (NNs) are employed to approximate unknown functions in the design procedure, and the separation technology is introduced here to tackle the problem induced from unknown time-delay items. The adaptive neural tracking control scheme is constructed by combining Lyapunov–Krasovskii functionals, NNs, the auxiliary system, the implicit function theory and the mean value theorem along with the dynamic surface control technique. Also, it is proven that the strategy guarantees tracking errors converge to a small neighbourhood around the origin by appropriate choice of design parameters and all signals in the closed-loop system uniformly ultimately bounded. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Time delay is a phenomenon which is common in signal processing, communication, control applications, etc. The special feature of time delay that makes it attractive is that it is a commonly faced problem in many systems. A literature search on time-delay identification highlights the fact that most studies focused on numerical solutions. In this study, a novel online adaptive time-delay identification technique is proposed. This technique is based on an adaptive update law through a minimum-maximum strategy which is firstly applied to time-delay identification. In the design of the adaptive identification law, Lyapunov-based stability analysis techniques are utilised. Several numerical simulations were conducted with Matlab/Simulink to evaluate the performance of the proposed technique. It is numerically demonstrated that the proposed technique works efficiently in identifying both constant and disturbed time delays, and is also robust to measurement noise. [ABSTRACT FROM AUTHOR]