Average Impulsive Interval Research Articles

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

In this paper, the impulsive effects on the finite-time stability of neural networks with time-varying delay are considered. Several novel criteria which govern the systems considered are finite-time stable are obtained by the idea of Lyapunov–Krasovskii functional and the average impulsive interval method. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities which can be easily checked by Matlab LMI toolbox. The results proposed show that the model can achieve stable in finite time with stabilizing impulsive effects on one hand, and it can preserve the finite-time stability property in presence of destabilizing impulses on the other hand. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

Stability analysis for a class of random nonlinear impulsive systems

Summary In this paper, the problem of noise-to-state stability (NSS) and globally asymptotic stability (GAS) is investigated for a class of nonlinear systems with random disturbances and impulses, where the random noises have finite second-order moments and the so-called random impulses mean that impulse ranges are driven by a sequence of random variables. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random nonlinear impulsive systems. Next, when the continuous dynamics are stable but the impulses are destabilizing, the NSS and GAS of random nonlinear impulsive systems are examined by the average impulsive interval approach. Then, when the continuous dynamics are unstable but the impulses are stabilizing, it is shown that the NSS and GAS can be retained by using the reverse average impulsive interval approach. Finally, the theoretical findings are substantiated with illustrative examples. Copyright © 2016 John Wiley & Sons, Ltd.

Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects

This note considers globally finite-time synchronization of coupled networks with Markovian topology and distributed impulsive effects. The impulses can be synchronizing or desynchronizing with certain average impulsive interval. By using $M$ -matrix technique and designing new Lyapunov functions and controllers, sufficient conditions are derived to ensure the synchronization within a setting time, and the conditions do not contain any uncertain parameter. It is demonstrated theoretically and numerically that the number of consecutive impulses with minimum impulsive interval of the desynchronizing impulsive sequence should not be too large. It is interesting to discover that the setting time is related to initial values of both the network and the Markov chain. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

AbstractThis paper is concerned with the exponential stability analysis of stochastic delayed systems with impulsive effects. By using the average impulsive interval approach, and together with comparison lemma and Razumikhin techniques, sufficient conditions ensuring the moment exponential stability of the systems under consideration are established. A stability criterion for non‐delayed stochastic systems with impulses is also derived as a corollary. Compared with the existing stability results in the literature, which are usually based on the supremum or infimum of impulsive intervals, the results reported in this paper are less conservative. Two illustrative examples are provided to validate the effectiveness and advantages of our theoretical results.

Stability and L2‐gain analysis for switched singular linear systems with jumps

In this paper, we study the stability problems and L2‐gain analysis for switched singular linear systems with jumps. Based on the concept of average impulsive interval, some novel sufficient conditions on the stability and L2‐gain for switched singular linear systems with jumps are developed. Two examples are given to illustrate the effectiveness of the results. Copyright © 2016 John Wiley & Sons, Ltd.

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

In this paper, the problem of exponential cluster synchronization of general hybrid-coupled impulsive dynamical networks with internal delay and delayed coupling is investigated. A more general delayed coupling term including different transmission delay and self-feedback delay is taken into account. By using average impulsive interval approach and the analysis technique, some novel globally exponential cluster synchronization criteria are derived analytically. It is noted that the internal delay, transmission delay and self-feedback delay are all time-varying and can be different from each other, the inner connecting matrices are not demanded to be diagonal and the coupling matrices are not restricted to be symmetric or irreducible, more consistent with the realistic networks. Particularly, it is shown that the derived cluster synchronization criteria are simultaneously applicable for studying general delayed dynamical networks with synchronizing impulses or desynchronizing impulses. Numerical examples are finally given to illustrate the effectiveness of the obtained theoretical results.

Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control

This paper investigates the issue of exponential synchronization for a class of nonlinearly coupled complex networks with hybrid time-varying delays by applying impulsive control protocol. It should be mentioned we need not to assume the synchronization state since it may be difficult to find an appropriate function or dynamics to describe the synchronization manifold. By employing the Lyapunov method combined with average impulsive interval as well as the comparison principle, a set of simple and easily verifiable sufficient conditions are derived to guarantee the exponential synchronization for any initial values. Meanwhile, the exponential convergence rate can be specified through the analysis of the networks. Additionally, some numerical examples are given to verify the effectiveness of our theoretical results.

Input-to-state stability of impulsive stochastic delayed systems under linear assumptions

In this paper, the input-to-state stability (ISS), integral-ISS (iISS) and stochastic-ISS (SISS) are investigated for impulsive stochastic delayed systems. By means of the Lyapunov–Krasovskii function and the average impulsive interval approach, the conditions for ISS-type properties are derived under linear assumptions, respectively, for destabilizing and stabilizing impulses. It is shown that if the continuous stochastic delayed system is ISS and the impulsive effects are destabilizing, then the hybrid system is ISS with respect to a lower bound of the average impulsive interval. Moreover, it is unveiled that if the continuous stochastic delayed system is not ISS, the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval. An improved comparison principle is developed for impulsive stochastic delayed systems, which facilitates the derivations of our results for ISS/iISS/SISS. An example of networked control systems is provided to illustrate the effectiveness of the proposed results.

Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers

This paper presents an analytical study of outer synchronization of partially coupled dynamical networks via pinning impulsive controller. At first, more realistic drive-response partially coupled networks are established. Then, based on the regrouping method, some efficient and less conservative synchronization criteria are derived and developed in terms of average impulsive interval. Our results show that, by impulsively controlling a crucial fraction of nodes in the response network, the outer synchronization can be achieved. Finally, illustrated examples are given to verify the effectiveness of the proposed strategy.

Synchronization analysis of hybrid-coupled delayed dynamical networks with impulsive effects: A unified synchronization criterion

This paper addresses the problem of globally exponential synchronization for a class of general hybrid-coupled impulsive delayed dynamical networks with both internal delay and coupling delay. A more general delayed coupling term involving the transmission delay and self-feedback delay is considered. Additionally, two types of impulses occurred in the states of nodes are taken into account: (i) synchronizing impulses defined as they can enhance the synchronization of dynamical networks; and (ii) desynchronizing impulses meaning that they can suppress the synchronization of dynamical networks. By establishing an improved impulsive differential inequality derived based on the average impulsive interval approach, a simpler and less conservative unified globally exponential synchronization criterion is obtained, which is simultaneously effective for synchronizing and desynchronizing impulses. It is shown that the obtained criterion is closely related with impulse strengths, average impulsive interval, and topology structure of the networks. Finally, numerical examples including a typical nearest-neighbor unidirectional coupled network and a scale-free network are given to demonstrate the applicability and efficiency of the theoretical results.

Stability and L 2 ‐gain performance for non‐linear switched impulsive systems

In this study, the authors investigate the exponential stability and L 2-gain for a class of non-linear switched impulsive systems with time-varying disturbances. Using the concept of average impulsive interval incorporated with a piecewise Lyapunov function, some new stability criteria and disturbance attenuation properties are presented. The derived criteria are theoretically proved to be less conservative than some existing results. A numerical example as well as its simulation is given to illustrate the effectiveness of the obtained results.

Exponential stability of impulsive positive systems with mixed time‐varying delays

This study addresses the problem of exponential stability for a class of impulsive positive systems with mixed time-varying delays. A delayed impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. By using a copositive Lyapunov–Krasovskii functional and the average impulsive interval method, a sufficient criterion of global exponential stability for delayed impulsive positive systems is established in terms of linear programming problems. A numerical example is given to show the effectiveness of the proposed method.

Exponential synchronization of impulsive discrete-time complex networks with time-varying delay

In this paper, the exponential synchronization of discrete-time complex networks with time-varying delay is investigated. Based on the Lyapunov function method and the Razumikhin technique, several synchronization criteria are derived for exponential synchronization of impulsive discrete-time complex networks. Using the concept of “average impulsive interval”, the derived results are proved to be effective in dealing with synchronizing and desynchronizing impulses. Several numerical simulation examples are provided to demonstrate the effectiveness of the proposed approach. Moreover, the simulation results show that the criteria are less conservative than the existing results considering the upper or lower of impulsive intervals.

Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach

In this paper, a novel impulsive control law is proposed for synchronization of stochastic discrete complex networks with time delays and switching topologies, where average dwell time and average impulsive interval are taken into account. The side effect of time delays is estimated by Lyapunov–Razumikhin technique, which quantitatively gives the upper bound to increase the rate of Lyapunov function. By considering the compensation of decreasing interval, a better impulsive control law is recast in terms of average dwell time and average impulsive interval. Detailed results from a numerical illustrative example are presented and discussed. Finally, some relevant conclusions are drawn.

Synchronization analysis of directed complex networks with time-delayed dynamical nodes and impulsive effects

In this paper, the effect of impulses on the synchronization of a class of general delayed dynamical networks is analyzed. The network topology is assumed to be directed and weakly connected with a spanning tree. Two types of impulses occurred in the states of nodes are considered: (i) synchronizing impulses meaning that they can enhance the synchronization of dynamical networks; and (ii) desynchronizing impulses defined as the impulsive effects can suppress the synchronization of dynamical networks. For each type of impulses, some novel and less conservative globally exponential synchronization criteria are derived by using the concept of average impulsive interval and the comparison principle. It is shown that the derived criteria are closely related with impulse strengths, average impulsive interval, and topology structure of the networks. The obtained results not only can provide an effective impulsive control strategy to synchronize an arbitrary given delayed dynamical network even if the original network may be asynchronous itself but also indicate that under which impulsive perturbations globally exponential synchronization of the underlying delayed dynamical networks can be preserved. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Stochastic Synchronization of Complex Networks With Mixed Impulses

In this paper, stochastic synchronization is studied for complex networks with delayed coupling and mixed impulses. Mixed impulses are composed of desynchronizing and synchronizing impulses. The delayed coupling term involves transmission delay and self-feedback delay. By using the average impulsive interval approach and the comparison principle, several conditions are derived to guarantee that exponential synchronization of complex networks is achieved in the mean square. The derived conditions are closely related to the impulsive strengths, the frequency of impulse occurrence, and the coupling structure of complex networks. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.

A new impulsive synchronization criterion for T–S fuzzy model and its applications

This paper focuses on the problem of impulsive synchronization of T–S fuzzy systems. A new synchronization criterion is derived for T–S fuzzy systems by utilizing the concept of average impulsive interval. The proposed impulsive control scheme has a simple control structure, and is theoretically and numerically proved to be less conservative than some existing results. The method is also illustrated by applying to Lorenz system, Rössler’s system as well as permanent magnet synchronous motors system.

Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control

In this paper, the global exponential synchronization of delayed complex dynamical networks with nonidentical nodes and stochastic perturbations is studied. By combining adaptive control and impulsive control schemes, the considered network can be synchronized onto any given goal dynamics. The adaptive control is discontinuous and can overcome the unknown difference between dynamical nodes and goal system. As for the impulsive control, the concept named “average impulsive interval” with “elasticity number” of impulsive sequence is utilized to get less conservative synchronization criterion. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.

Exponential Stability of Impulsive Stochastic Delay Differential Systems

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.

Impulsive Synchronization of Nonlinearly Coupled Complex Networks

This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low‐dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive interval. A numerical example is given to illustrate the effectiveness and feasibility of the proposed methods and results.