Impulsive Interval Research Articles

Input-to-state stability of stochastic nonlinear system with delayed impulses.

Stochastic input-to-state stability (SISS) of the stochastic nonlinear system has received extensive research. This paper aimed to investigate SISS of the stochastic nonlinear system with delayed impulses. First, when all subsystems were stable, using the average impulsive interval method and Lyapunov approach, some theoretical conditions ensuring SISS of the considered system were established. The SISS characteristic of the argumented system with both stable and unstable subsystems was also discussed, then the stochastic nonlinear system with multiple delayed impulse jumps was considered and SISS property was explored. Additionally, it should be noted that the Lyapunov rate coefficient considered in this paper is positively time-varying. Finally, several numerical examples confirmed validity of theoretical results.

Finite-Time Boundedness of Impulsive Delayed Reaction-Diffusion Stochastic Neural Networks.

Considering the impulsive delayed reaction-diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.

Synchronization of Time-Delay Coupled Neural Networks With Stabilizing Delayed Impulsive Control.

This brief studies the distributed synchronization of time-delay coupled neural networks (NNs) with impulsive pinning control involving stabilizing delays. A novel differential inequality is proposed, where the state's past information at impulsive time is effectively extracted and used to handle the synchronization of coupled NNs. Based on this inequality, the restriction that the size of impulsive delay is always limited by the system delay is removed, and the upper bound on the impulsive delay is relaxed, which is improved the existing related results. By using the methods of average impulsive interval (AII) and impulsive delay, some relaxed criteria for distributed synchronization of time-delay coupled NNs are obtained. The proposed synchronization conditions do not impose on the upper bound of two consecutive impulsive signals, and the lower bound is more flexible. Moreover, our results reveal that the impulsive delays may contribute to the synchronization of time-delay systems. Finally, typical networks are presented to illustrate the advantage of our delayed impulsive control method.

Finite-Time Synchronization of Complex Dynamical Networks via a Novel Hybrid Controller.

The issue of finite-time synchronization (FTS) of complex dynamical networks (CDNs) is investigated in this article. A new control strategy coupling weak finite-time control and finite times of impulsive control is proposed to realize the FTS of CDNs, where the impulses are synchronizing and restricted by maximal impulsive interval (MII), differing from the existing results. In this framework, several global and local FTS criteria are established by using the concept of impulsive degree. The times of impulsive control in the controllers and the settling time, which are all dependent on initial values, are derived optimally. A technical lemma is developed, reflecting the core idea of this article. A simulation example is given to demonstrate the main results finally.

Synchronization of time-delay systems with impulsive delay via an average impulsive estimation approach.

We investigated synchronization of dynamic systems with mixed delays and delayed impulses. Using impulsive control method and the average impulsive interval approach, several Lyapunov sufficient conditions were given for ensuring synchronization in terms of impulsive perturbation and impulsive control, respectively. The derived conditions indicated that delays in continuous dynamical systems were flexible under impulsive perturbation and were not strictly dependent on the size of impulsive delays, and they may have a potential impact on synchronization of the considered system. In addition, applying the proposed concepts of average positive impulsive estimation and average impulsive estimation, we integrated the information in impulsive delay into the rate coefficient to eliminate the limitation of having the same threshold at each impulse point, while the impulsive delay maintained the synchronization effect. This was an improvement on the previous results obtained. Finally, we provided two numerical examples to illustrate the validity of our results.

Synchronization results for uncertain complex-valued neural networks under delay-dependent flexible impulsive control

This paper is concerned with error estimation between two non-identical uncertain complex-valued neural networks (CVNNs) based on delay-dependent flexible impulsive control (DDFIC). By implementing the ideas of average impulsive delay (AID) and average impulsive interval (AII), we established a new delay dependent flexible impulsive delay differential inequality to reduce the error exponentially for the proposed CVNNs. Moreover, we obtained some new criteria to reduce error exponentially and robust exponentially with regard to linear matrix inequalities (LMIs) by using the Lyapunov function for the proposed CVNNs, and we also designed the DDFIC gains by solving LMIs. The DDFIC effectively reduced the errors for the proposed networks and is represented using numerical examples along with its simulations.

Matrix measure-based distributed impulsive consensus on nonlinear multi-agent systems with mixed time-varying delays

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis.

Finite-time quasi-synchronization of multi-layer heterogeneous networks with distributed hybrid control

In this paper, the finite-time quasi-synchronization of a multi-layer heterogeneous network with a leader node is studied. A novel distributed control approach that incorporates impulsive control is introduced to achieve finite-time quasi-synchronization of the whole network. The control protocol is distributed, the impulses are synchronized, and the maximum time interval of impulses is bounded. Within this framework and based on the maximum impulsive interval, a finite-time quasi-synchronization criterion for the multi-layer heterogeneous network is established. A close relationship between the settling time and the maximum impulsive interval is discovered. Simulations are shown for illustration and verification.

Mean square exponential stabilization analysis of stochastic neural networks with saturated impulsive input

The exponential stabilization of stochastic neural networks in mean square sense with saturated impulsive input is investigated in this paper. Firstly, the saturated term is handled by polyhedral representation method. When the impulsive sequence is determined by average impulsive interval, impulsive density and mode-dependent impulsive density, the sufficient conditions for stability are proposed, respectively. Then, the ellipsoid and the polyhedron are used to estimate the attractive domain, respectively. By transforming the estimation of the attractive domain into a convex optimization problem, a relatively optimum domain of attraction is obtained. Finally, a three-dimensional continuous time Hopfield neural network example is provided to illustrate the effectiveness and rationality of our proposed theoretical results.

Input-to-state stability of stochastic differential systems with hybrid delay-dependent impulses

This paper discusses the pth moment input-to-state stability(p-ISS) and pth moment integral input-to-state stability(p-iISS) for impulsive stochastic systems with time-varying delays and hybrid delayed impulses. With the Lyapunov method and some techniques, the criteria for the impulsive stochastic system p-ISS and p-iISS are established under two common hypotheses, while our criterion allows the time delay to be less than, equal to, or greater than the length of the impulsive interval. The results show that time delay, intensity, and density of hybrid delayed impulses are the main factors affecting the p-ISS and p-iISS of the system; In other words, changing one or more of these factors can stabilize the unstable system. In addition, if both delayed impulses and continuous dynamics are stable, then time delay does not affect the stability of impulsive stochastic systems. The impulsive systems may be p-ISS and p-iISS when unstable delayed impulses perturb the stable continuous dynamics. Finally, two examples are presented to show the validity and correctness of results.

Bipartite secure synchronization for dynamic networks under deception attacks via delay-dependent impulsive control

In this paper, we investigate mean-square bounded bipartite synchronization of coupled dynamic networks subject to deception attacks, especially under directed/undirected signed interconnection structures. An impulsive secure control input involving stabilizing delays is proposed. The average impulsive delay (AID) method is used to fetch the information of time delay existing in impulses, and then this information is effectively integrated to mitigate the negative effects of deception attacks on synchronization. A concept of stochastic variables is introduced to serve as a measure of attack success when delayed impulsive control signals are replaced with false data from the impulsive controller-to-actuator. To achieve desired synchronization performance under deception attacks, the gains of pinning impulsive control, the average impulsive interval (AII), AID and the attack intensity are co-designed. An upper bound for synchronization errors is provided, which can be adjusted with multiple adjustable parameters. In addition, the AII and AID methods are used to remove the restriction on upper/lower bounds of two consecutive impulsive instants. Finally, numerical examples are given to illustrate the validity of the theoretical results.

An Impulse-Quantizing Synchronization Approach for Mixed Continuous-Discrete Complex Networks

This paper presents synchronization of mixed continuous-discrete complex network via impulse-quantizing approach. A delay-partitioning group strategy is proposed and impulse-quantizing control is designed to derive theoretical criteria ensuring scale-type synchronization of complex networks. Our results show that synchronization of mixed continuous-discrete complex networks can be realized by controlling delay-partitioning subgroup nodes with impulsive quantization. The theoretical results give scale-limited sufficient conditions for quantized synchronization relying on control gains, impulsive intervals, and delays. A numerical simulation is given to demonstrate the effectiveness of the theoretical results.

Stability of nonlinear impulsive systems with non-uniformly distributed packet loss

This study focuses mainly on the stability of a class of nonlinear systems with impulsive disturbance. In particular, we consider the possible non-uniformly distributed packet loss phenomenon in the controller-to-actuator channel. This packet loss is described by a characterization scenario in the average sense, known as the average packet loss interval (APLI). In this scenario, an average allocation strategy between the number of impulsive sampling intervals and the length of packet loss intervals is established. This implies that the limitations on the proportion or the upper bound of packet loss intervals can be relaxed. A sampled-data control is put forward based on impulsive disturbance, which not only brings better control performance but also reduces conservatism. In view of the Halanay inequality, the number of subsystem switchings caused by packet loss is allowed to be arbitrary. Based on the elastic constraint relationships established between system parameters and APLI, a series of conditions guaranteeing the globally uniformly exponential stability (GUES) are provided. Further, the admissible packet loss intervals can be estimated on an average basis by solving an algebraic inequality. Finally, a numerical example is discussed to demonstrate the validity of our study.

Novel Synchronization Criteria for Non-Dissipative Coupled Networks with Bounded Disturbances and Time-Varying Delays of Unidentified Bounds via Impulsive Sampling Control

The μ−synchronization issues of non-dissipative coupled networks with bounded disturbances and mixed delays are studied in this article. Different from existing works, three kinds of time delays, including internal delays, coupling delays, and impulsive sampling delays, have unidentified bounds and even evolve towards infinity over time, making the concerned network more practical. Considering μ−stability theory and impulse inequality techniques, a hybrid non-delayed and time-delayed impulsive controller including both current and historical state information is designed, and several novel sufficient conditions are derived to make nonlinear complex networks achieve μ−synchronization. Moreover, not only can the constriction of dissipative coupling conditions on network topology be relaxed, but also the restriction of various time delays on impulsive intervals can be weakened, which makes the theoretical achievements in this article more general than the previous achievements. Ultimately, numerical simulations confirm the effectiveness of our results.

Stability of multi-link delayed impulsive stochastic complex networks with Markovian switching

This article presents an analysis of p-th moment exponential stability for a class of stochastic functional differential systems with Markovian switching on complex multi-link networks using multi-delayed impulsive control. The multi-delayed impulsive control scheme implies that the impulsive jumps are related to multiple past states of the systems, which increases the complexity of the analysis. Additionally, single-link networks are extended to complex multi-link networks, which are more extensive. By combining graph theory and the Razumikhin method, several criteria for achieving p-th moment exponential stability for systems are derived. The criteria are related to the maximum upper bound of delays, impulsive interval, and network topology. Subsequently, the stability of multi-link stochastic complex networks with time delays and Markovian switching is studied using delayed impulsive control. Finally, the exponential stability of a class of stochastic coupled multi-link oscillators with Markovian switching is analyzed, and several numerical simulations are provided to verify the validity of the theoretical results.

Local Synchronization of Directed Lur'e Networks With Coupling Delay via Distributed Impulsive Control Subject to Actuator Saturation.

This article studies the local exponential synchronization synthesis problem of directed Lur'e networks with coupling time-varying delay under the distributed impulsive control subject to actuator saturation. First, by utilizing proof by contradiction, impulsive comparison principle, and latest improved convex hull representation of saturation function, some delay-independent sufficient criteria for local exponential synchronization are presented in the form of bilinear matrix inequalities. Meanwhile, a novel method with less conservatism is developed to estimate the domain of attraction, which is radically different from the traditional method by means of contractive invariant set. Second, optimization problems constrained by the transformed linear matrix inequalities are established to acquire the maximum estimates of both the domain of attraction and average impulsive interval (AII), which are conveniently solved by the YALMIP toolbox in MATLAB software. Finally, a numerical simulation is rendered to demonstrate the effectiveness and advantages of the proposed theoretical results.

Lyapunov-based stability of time-triggered impulsive logical dynamic networks

In this paper, we consider the stability of impulsive logical dynamic systems (ILDNs) from two aspects: impulsive disturbance and impulsive control. The existing results on the stability of ILDNs only consider the stability of ILDNs under a given impulsive instant sequence (IIS), which has some limitations and motivates us to consider the stability of ILDNs under any IIS. By constructing a merged ILDN, under the assumption that the non-impulsive process and impulsive process are all globally stable, a necessary and sufficient condition on the stability of ILDNs under any IIS is proposed at first. Unfortunately, the obtained result is too restrictive, and in practice, it is not common that a stable LDN is still stable under any IIS. The fact is that for any stable LDN, there exist some IISs such that its stability is destroyed, and these IISs are called impulsive disturbances; for any unstable LDN, there exist some IISs such that the stability can be achieved, and these IISs are called impulsive control. To investigate the stability of ILDNs, the concept of average impulsive interval is first introduced to ILDNs, and several sufficient conditions are proposed to ensure the stability of LDNs under the time-triggered IISs with the property of average impulsive interval. Moreover, the obtained results are applied to the set stability of ILDNs.

Exponential stability of time‐delay systems with flexible delayed impulse

AbstractThe problem of exponential stability for time‐delay systems with flexible delayed impulse control is investigated. Unlike the conventional Razumikhin‐type inequality, variable parameter based on the flexible impulsive gain is introduced. Sufficient conditions for exponential stability are developed for a class of time‐delay systems, for which the size of delay is not limited by impulsive intervals. A flexible impulse control scheme is developed by utilizing the flexible impulsive gain and time‐varying delays. When the system is disturbed by the impulse interferences, both the impulse gain and impulse delay can be adjusted accordingly to make the system exponential stable. The effectiveness of the present results is illustrated by two numerical examples and an application.

Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

Instability of stochastic differential systems with impulsive effects

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