Stability of nonlinear variable-time impulsive differential systems with delayed impulses

Abstract This paper investigates the stability of nonlinear variable-time impulsive differential systems with delayed impulses. By using the comparison principle, the Lyapunov method and inequality techniques, some sufficient conditions for quasi-uniformly asymptotic stability and quasi-exponential stability of a given solution of variable-time impulsive differential systems with delayed impulses are established.

[1]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Chuandong Li,et al.  Stability of nonlinear systems with variable-time impulses: B-equivalence method , 2017 .

[3]  Chuandong Li,et al.  Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects , 2020, Neural Networks.

[4]  Wei Xing Zheng,et al.  Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays , 2009, Autom..

[5]  Yan-Jun Liu,et al.  Neural Network Controller Design for a Class of Nonlinear Delayed Systems With Time-Varying Full-State Constraints , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Zhidong Teng,et al.  Dynamic analysis of an SIR epidemic model with state dependent pulse vaccination , 2012 .

[7]  Xinzhi Liu,et al.  Quasi stability via lyapunov functions for impulsive differential systems , 1988 .

[8]  Martin Bohner,et al.  Impulsive differential equations: Periodic solutions and applications , 2015, Autom..

[9]  Kexue Zhang,et al.  Stabilization of time-delay neural networks via delayed pinning impulses , 2016 .

[10]  Junlin Xiong,et al.  Stability Analysis of Impulsive Switched Time-Delay Systems With State-Dependent Impulses , 2019, IEEE Transactions on Automatic Control.

[11]  Wei Xing Zheng,et al.  Exponential stability of nonlinear time-delay systems with delayed impulse effects , 2011, Autom..

[12]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Tracking Control for Strict-Feedback Nonlinear Systems With Unknown Control Gain Functions , 2020, IEEE Transactions on Cybernetics.

[13]  Xinzhi Liu,et al.  Existence and continuability of solutions for differential equations with delays and state-dependent impulses , 2002 .

[14]  Habib Fardoun,et al.  Stability Analysis of Delayed Impulsive Systems and Applications , 2018, Circuits Syst. Signal Process..

[15]  Li Ma,et al.  Observer-based adaptive fuzzy tracking control of MIMO switched nonlinear systems preceded by unknown backlash-like hysteresis , 2019, Inf. Sci..

[16]  Chuandong Li,et al.  Synchronization of coupled memristive chaotic circuits via state-dependent impulsive control , 2017 .

[17]  Wei Xing Zheng,et al.  Impulsive Stabilization and Impulsive Synchronization of Discrete-Time Delayed Neural Networks , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Jian-an Fang,et al.  Synchronization of hybrid impulsive and switching dynamical networks with delayed impulses , 2016 .

[19]  Guanrong Chen,et al.  Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback , 2009 .

[20]  Xiaoli Zhang,et al.  Effect of delayed impulses on input-to-state stability of nonlinear systems , 2017, Autom..

[21]  Wei Xing Zheng,et al.  Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[23]  Xiaodi Li,et al.  Exponential Stability of Nonlinear Systems With Delayed Impulses and Applications , 2019, IEEE Transactions on Automatic Control.

[24]  Xinzhi Liu,et al.  Analyzing the Robustness of Impulsive Synchronization Coupled by Linear Delayed Impulses , 2009, IEEE Transactions on Automatic Control.

[25]  Xinzhi Liu,et al.  Stability Criteria for Impulsive Systems With Time Delay and Unstable System Matrices , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  Chuandong Li,et al.  Global exponential stability of high-order Hopfield neural networks with state-dependent impulses , 2020 .

[27]  Qiankun Song,et al.  Effects of State-Dependent Impulses on Robust Exponential Stability of Quaternion-Valued Neural Networks Under Parametric Uncertainty , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[28]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[29]  Martin Bohner,et al.  Almost periodic solutions of Cohen-Grossberg neural networks with time-varying delay and variable impulsive perturbations , 2020, Commun. Nonlinear Sci. Numer. Simul..

[30]  Chuandong Li,et al.  Fixed-time stabilization of impulsive Cohen-Grossberg BAM neural networks , 2018, Neural Networks.

[31]  Xinzhi Liu,et al.  Input-to-state stability of impulsive and switching hybrid systems with time-delay , 2011, Autom..

[32]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[33]  Chuandong Li,et al.  Periodicity and stability for variable-time impulsive neural networks , 2017, Neural Networks.

[34]  Huamin Wang,et al.  Stability of impulsive delayed linear differential systems with delayed impulses , 2015, J. Frankl. Inst..

[35]  Yang Tang,et al.  Synchronization of Stochastic Dynamical Networks Under Impulsive Control With Time Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Xiaodi Li,et al.  Sufficient Stability Conditions of Nonlinear Differential Systems Under Impulsive Control With State-Dependent Delay , 2018, IEEE Transactions on Automatic Control.

[37]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[38]  Chuandong Li,et al.  Existence of solution, pulse phenomena and stability criteria for state-dependent impulsive differential equations with saturation , 2019, Commun. Nonlinear Sci. Numer. Simul..

[39]  Marat Akhmet,et al.  Neural Networks with Discontinuous/Impact Activations , 2013 .

[40]  Joao P. Hespanha,et al.  Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays , 2009 .

[41]  Sanyi Tang,et al.  State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences , 2005, Journal of mathematical biology.

[42]  Xiaodi Li,et al.  Recent progress in impulsive control systems , 2019, Math. Comput. Simul..

[43]  Xinzhi Liu,et al.  Delay-Dependent Impulsive Distributed Synchronization of Stochastic Complex Dynamical Networks With Time-Varying Delays , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[44]  Kexue Zhang,et al.  Stabilization of nonlinear time-delay systems: Distributed-delay dependent impulsive control , 2018, Syst. Control. Lett..

[45]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[46]  Liangliang Li,et al.  Delayed-impulsive control for difference systems with actuator saturation and its synchronisation application , 2019 .

[47]  Mustafa Sayli,et al.  Global robust asymptotic stability of variable-time impulsive BAM neural networks , 2014, Neural Networks.

[48]  Peter Xiaoping Liu,et al.  Adaptive Fuzzy Finite-Time Control of Nonlinear Systems With Actuator Faults , 2020, IEEE Transactions on Cybernetics.

[49]  Quanxin Zhu,et al.  Stabilization of stochastic functional differential systems with delayed impulses , 2019, Appl. Math. Comput..

[50]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[51]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Decentralized Optimal Control Design for Strict-Feedback Nonlinear Large-Scale Systems , 2018, IEEE Transactions on Fuzzy Systems.

[52]  Kexue Zhang,et al.  Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses , 2016, Autom..

[53]  Jinde Cao,et al.  Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications , 2020, IEEE Transactions on Cybernetics.

[54]  Jianquan Lu,et al.  Some recent results of analysis and control for impulsive systems , 2020, Commun. Nonlinear Sci. Numer. Simul..

[55]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[56]  Huanqing Wang,et al.  Adaptive neural control for non-strict-feedback nonlinear systems with input delay , 2020, Inf. Sci..

[57]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[58]  Lansun Chen,et al.  Studies on the dynamics of a continuous bioprocess with impulsive state feedback control , 2010 .

[59]  Kexue Zhang,et al.  Consensus of multi-agent systems via hybrid impulsive protocols with time-delay , 2018, Nonlinear Analysis: Hybrid Systems.

[60]  Marat Akhmet,et al.  Principles of Discontinuous Dynamical Systems , 2010 .

[61]  Xin Wang,et al.  Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window , 2017, Neural Computing and Applications.