Unified Stability Criteria of Random Nonlinear Time-Varying Impulsive Switched Systems

This paper investigates the problem of noise-to-state practical stability in mean (NSpS-M) (which is a natural generalization of noise-to-state stability in mean) and the problem of almost sure global asymptotic stability (GAS a.s.) for a class of random nonlinear time-varying impulsive switched systems. By using the notions of average impulsive switched interval and Poisson process, unified sufficient stability criteria on NSpS-M and GAS a.s. are derived. Two remarkable distinctions from the existing results lie in that: (1) stabilizing, inactive and destabilizing impulses are simultaneously considered; (2) the coefficient of the derivative of a Lyapunov function is allowed to be a time-varying function which can be both positive and negative and may even be unbounded. As an accompaniment, a less conservative unified criterion on NSpS-M for a special case is also presented by taking into account the stabilization role of the gain constant of the time-varying coefficient. Two examples are provided to illustrate the effectiveness of our derived criteria.

[1]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[2]  Tomohisa Hayakawa,et al.  Event-Triggered Output Feedback Control Resilient Against Jamming Attacks and Random Packet Losses , 2015 .

[3]  Guangdeng Zong,et al.  Exponential stability for generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching , 2018, Nonlinear Analysis: Hybrid Systems.

[4]  Horacio J. Marquez,et al.  Controllability and Observability for a Class of Controlled Switching Impulsive Systems , 2008, IEEE Transactions on Automatic Control.

[5]  Peng Shi,et al.  Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $ , 2010, IEEE Transactions on Automatic Control.

[6]  Kiyosi Itô.  On a stochastic integral equation , 1946 .

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

[8]  Ping Li,et al.  Disturbance Observer-Based Fault-Tolerant Adaptive Control for Nonlinearly Parameterized Systems , 2019, IEEE Transactions on Industrial Electronics.

[9]  Guangdeng Zong,et al.  Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[10]  Hamid Reza Karimi,et al.  Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[11]  Quanxin Zhu,et al.  Stability analysis of semi-Markov switched stochastic systems , 2018, Autom..

[12]  Junwu Zhu,et al.  Adaptive consensus control of leader-following systems with transmission nonlinearities , 2019, Int. J. Control.

[13]  Hamid Reza Karimi,et al.  Asynchronous Finite-Time Filtering of Networked Switched Systems and its Application: an Event-Driven Method , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Shengyuan Xu,et al.  Stability analysis for a class of random nonlinear impulsive systems , 2017 .

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

[16]  Hangli Ren,et al.  Finite-time stability of interconnected impulsive switched systems , 2015, 2015 34th Chinese Control Conference (CCC).

[17]  Shengyuan Xu,et al.  Sampled-data controller design and stability analysis for nonlinear systems with input saturation and disturbances , 2019, Appl. Math. Comput..

[18]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[19]  Quanxin Zhu,et al.  pth Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching , 2014, J. Frankl. Inst..

[20]  Zhaojing Wu,et al.  Stability Criteria of Random Nonlinear Systems and Their Applications , 2015, IEEE Transactions on Automatic Control.

[21]  Hao Shen,et al.  Quantized Output Feedback Control for Stochastic Semi-Markov Jump Systems With Unreliable Links , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Ju H. Park,et al.  Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays , 2010 .

[23]  Jason Gu,et al.  Global High-Order Sliding Mode Controller Design Subject to Mismatched Terms: Application to Buck Converter , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Peng Wang,et al.  Almost Output Regulation for Switched Positive Systems With Different Coordinates Transformations and its Application to a Positive Circuit Model , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Dong Yue,et al.  Observer-Based Fault Estimation for Discrete-Time Nonlinear Systems and Its Application: A Weighted Switching Approach , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  Yan Shi,et al.  Fuzzy adaptive control of a class of nonlinear systems with unmodeled dynamics , 2019, International Journal of Adaptive Control and Signal Processing.

[27]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[28]  Jorge Cortés,et al.  pth Moment Noise-to-State Stability of Stochastic Differential Equations with Persistent Noise , 2014, SIAM J. Control. Optim..

[29]  Shengyuan Xu,et al.  On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  C. Wen,et al.  Switched and Impulsive Systems: Analysis, Design, and Applications , 2005, IEEE Transactions on Automatic Control.

[31]  Yan Shi,et al.  Neural Networks-Based Distributed Adaptive Control of Nonlinear Multiagent Systems , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Feiqi Deng,et al.  New Criteria on $p$th Moment Input-to-State Stability of Impulsive Stochastic Delayed Differential Systems , 2017, IEEE Transactions on Automatic Control.

[33]  Corentin Briat,et al.  Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints , 2016, Autom..

[34]  P. Shi,et al.  Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems , 2017 .

[35]  Junlin Xiong,et al.  Lyapunov Conditions for Stability of Stochastic Impulsive Switched Systems , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  Bin Zhou,et al.  Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems , 2016, Autom..

[37]  Jinde Cao,et al.  Exponential H∞ Filtering for Continuous-Time Switched Neural Networks Under Persistent Dwell-Time Switching Regularity , 2020, IEEE Transactions on Cybernetics.

[38]  Mingyue Cui,et al.  Tracking controller design for random nonlinear benchmark system , 2017, J. Frankl. Inst..

[39]  Jiang-Wen Xiao,et al.  Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay , 2018 .

[40]  Hamid Reza Karimi,et al.  Fault Detection for Linear Discrete Time-Varying Systems With Multiplicative Noise: The Finite-Horizon Case , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Sing Kiong Nguang,et al.  Stability Analysis of Genetic Regulatory Networks With General Random Disturbances , 2019, IEEE Transactions on NanoBioscience.