Input/Output-to-State Stability of Impulsive Switched Systems With Time Delays

In this paper, we study the input/output-to-state stability (IOSS) of impulsive switched systems with time delays, where the derivative of Lyapunov functions are assumed to be time-varying and mode-dependent. Based on the Lyapunov-Razumikhin method and the mode-dependent average dwell time (MDADT) condition, some Rzaumikhin-type criteria for IOSS of impulsive switched systems with the coexistence of the destabilizing and stabilizing impulses are established. The derivative of Lyapunov functions of subsystems are allowed to be indefinite, which implies that the criteria can be applied to impulsive switched systems involving the coexistence of IOSS and non-IOSS subsystems. Furthermore, under mode-dependent conditions, the dwell time of each subsystem allows to be small or large enough. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed results.

[1]  Jinde Cao,et al.  Switching Laws Design for Stability of Finite and Infinite Delayed Switched Systems With Stable and Unstable Modes , 2018, IEEE Access.

[2]  Yun Zhang,et al.  A unified Razumikhin-type criterion on input-to-state stability of time-varying impulsive delayed systems , 2018, Syst. Control. Lett..

[3]  S. Dashkovskiy,et al.  Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods , 2010, 1011.2865.

[4]  Xiaodi Li,et al.  Review of stability and stabilization for impulsive delayed systems. , 2018, Mathematical biosciences and engineering : MBE.

[5]  Eduardo D. Sontag,et al.  Input-Output-to-State Stability , 2001, SIAM J. Control. Optim..

[6]  Ying Yang,et al.  Relaxed Conditions for the Input-to-State Stability of Switched Nonlinear Time-Varying Systems , 2017, IEEE Transactions on Automatic Control.

[7]  Daniel Liberzon,et al.  Input/output-to-state stability and state-norm estimators for switched nonlinear systems , 2012, Autom..

[8]  SERGEY DASHKOVSKIY,et al.  Input-to-State Stability of Nonlinear Impulsive Systems , 2012, SIAM J. Control. Optim..

[9]  Jinde Cao,et al.  Input-to-State Stability of Time-Varying Switched Systems With Time Delays , 2019, IEEE Transactions on Automatic Control.

[10]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[11]  Eduardo Sontag.  Input to State Stability: Basic Concepts and Results , 2008 .

[12]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

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

[14]  Qidi Wu,et al.  Less conservative conditions for asymptotic stability of impulsive control systems , 2003, IEEE Trans. Autom. Control..

[15]  R. Rakkiyappan,et al.  μ-stability criteria for nonlinear differential systems with additive leakage and transmission time-varying delays , 2018 .

[16]  Guopei Chen,et al.  New necessary and sufficient conditions for finite-time stability of impulsive switched linear time-varying systems , 2018 .

[17]  Wei Wang,et al.  Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics , 2012, Autom..

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

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

[20]  Kok Lay Teo,et al.  Exponential Stability With $L_{2}$-Gain Condition of Nonlinear Impulsive Switched Systems , 2010, IEEE Transactions on Automatic Control.

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

[22]  Lei Zhou,et al.  Event-Triggered Control of Continuous-Time Switched Linear Systems , 2019, IEEE Transactions on Automatic Control.

[23]  Zhi-Hong Guan,et al.  Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control , 2014, Autom..

[24]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[25]  Eduardo Sontag,et al.  Output-to-state stability and detectability of nonlinear systems , 1997 .

[26]  João Pedro Hespanha,et al.  Lyapunov conditions for input-to-state stability of impulsive systems , 2008, Autom..

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

[28]  Bin Zhou,et al.  On asymptotic stability of linear time-varying systems , 2016, Autom..

[29]  S. Dashkovskiy,et al.  Input-to-state stability of impulsive systems and their networks , 2017 .

[30]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[31]  Yong He,et al.  Indefinite Lyapunov functions for input-to-state stability of impulsive systems , 2018, Inf. Sci..

[32]  Jitao Sun,et al.  Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.