Stability Analysis of Impulsive Stochastic Nonlinear Systems

This paper studies stochastic input-to-state stability and stochastic global stability for impulsive stochastic nonlinear systems. Using fixed dwell-time condition and Lyapunov-based approach, sufficient conditions are established for the stability properties. Two cases are studied: 1) the case that the continuous dynamics is stable and 2) the case that the impulsive effects are stable. Furthermore, the relations among different dwell-time conditions are studied. Finally, two examples are used to illustrate the developed theory.

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

[2]  Hassan K. Khalil,et al.  Nonlinear Systems Third Edition , 2008 .

[3]  L. Rogers,et al.  Diffusions, Markov processes, and martingales , 1979 .

[4]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[5]  Junlin Xiong,et al.  Stability and stabilization of switched stochastic systems under asynchronous switching , 2016, Systems & control letters (Print).

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

[7]  Carlos Silvestre,et al.  Stability of networked control systems with asynchronous renewal links: An impulsive systems approach , 2013, Autom..

[8]  Enrique A. Medina,et al.  Reachability and observability of linear impulsive systems , 2008, Autom..

[9]  Jifeng Zhang,et al.  A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems , 2008 .

[10]  Yu Kang,et al.  Stochastic input-to-state stability of switched stochastic nonlinear systems , 2012, Autom..

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

[12]  Andrew R. Teel,et al.  Stability analysis for stochastic hybrid systems: A survey , 2014, Autom..

[13]  Jitao Sun,et al.  p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching , 2006, Autom..

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

[15]  R TeelAndrew,et al.  Stability analysis for stochastic hybrid systems , 2014 .

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

[17]  Debasish Chatterjee,et al.  Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions , 2006, SIAM J. Control. Optim..

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

[19]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Yang Tang,et al.  Input-to-state stability of impulsive stochastic delayed systems under linear assumptions , 2016, Autom..

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

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

[23]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[24]  Chen Lan.  Impulsive differential equations and life sciences , 2002 .

[25]  P. Shi,et al.  Stochastic stability and robust control for sampled-data systems with Markovian jump parameters , 2006 .