Input-to-state stability for nonlinear systems with stochastic impulses

Abstract In this study, the problem of input-to-state stability (ISS) is systematically investigated for nonlinear systems with stochastic impulses. First, the ISS problem is considered for systems, where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval. Then, the ISS problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density. Several different cases are considered, i.e., cases where the impulsive instants are satisfied by a renewal process, Poisson process, semi-Markov chain and Markov chain. An example of coordination of multi-agent systems is provided to illustrate the effectiveness of the proposed new stability criteria.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  Huijun Gao,et al.  Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses , 2015, Autom..

[3]  Debasish Chatterjee,et al.  Stabilizing Randomly Switched Systems , 2008, SIAM J. Control. Optim..

[4]  Sophie Tarbouriech,et al.  Stability analysis of linear impulsive delay dynamical systems via looped-functionals , 2017, Autom..

[5]  Gang Feng,et al.  Technical communique: Infinite horizon H2/H∞ control for stochastic systems with Markovian jumps , 2008 .

[6]  Patrizio Colaneri,et al.  Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach , 2016, IEEE Transactions on Automatic Control.

[7]  Wei Xing Zheng,et al.  Input-to-state stability for networked control systems via an improved impulsive system approach , 2011, Autom..

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

[9]  Debasish Chatterjee,et al.  Generalized switching signals for input-to-state stability of switched systems , 2016, Autom..

[10]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[11]  David J. Hill,et al.  Uniform stability and ISS of discrete-time impulsive hybrid systems , 2010 .

[12]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

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

[14]  Ljupco Kocarev,et al.  Tracking Control of Networked Multi-Agent Systems Under New Characterizations of Impulses and Its Applications in Robotic Systems , 2016, IEEE Transactions on Industrial Electronics.

[15]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[16]  W. P. M. H. Heemels,et al.  Periodic Event-Triggered Control for Linear Systems , 2013, IEEE Trans. Autom. Control..

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

[18]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

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

[20]  Junlin Xiong,et al.  Stability Analysis of Impulsive Stochastic Nonlinear Systems , 2017, IEEE Transactions on Automatic Control.

[21]  Jinde Cao,et al.  An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications , 2017, IEEE Transactions on Automatic Control.

[22]  Debasish Chatterjee,et al.  Studies on Stability and Stabilization of Randomly Switched Systems , 2007 .

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

[24]  J. Tsinias,et al.  Notions of exponential robust stochastic stability, ISS and their Lyapunov characterizations , 2003 .

[25]  Karl Henrik Johansson,et al.  Networked Control With Stochastic Scheduling , 2015, IEEE Transactions on Automatic Control.

[26]  Debasish Chatterjee,et al.  Towards ISS disturbance attenuation for randomly switched systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[27]  J. Tsinias.  Stochastic input-to-state stability and applications to global feedback stabilization , 1998 .

[28]  Debasish Chatterjee,et al.  On Stability of Randomly Switched Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[29]  Miroslav Krstic,et al.  Input-to-State Stability and Inverse Optimality of Linear Time-Varying-Delay Predictor Feedbacks , 2018, IEEE Transactions on Automatic Control.

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

[31]  Wei Xing Zheng,et al.  Impulsive stabilization of a class of singular systems with time-delays , 2017, Autom..

[32]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  John Lygeros,et al.  Stochastic Hybrid Systems: Research Issues and Areas , 2006 .

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

[35]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[36]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

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

[38]  Karl Henrik Johansson,et al.  Stochastic Sensor Scheduling for Networked Control Systems , 2012, IEEE Transactions on Automatic Control.

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

[40]  John Leth,et al.  Stochastic stability of systems with semi-Markovian switching , 2014, Autom..