Admissibility analysis of stochastic singular systems with Poisson switching

Abstract This paper addresses the mean square admissibility problem for a class of stochastic singular systems with Poisson switching. By using H -representation approach, we show the equivalence between mean square admissibility and robust admissibility of a deterministic system, which is an extension of the result in the case of deterministic system [1]. Based on multiple Lyapunov functions and matrix decomposition approaches, some easily verifiable sufficient conditions without equality constraint are established and can be conveniently used to state feedback controller design. Some admissibility criteria are constructed for linear singular systems with Poisson switching. Three examples including a RLC circuit and a mass-spring-damper system are introduced to demonstrate the validity of the theoretical results.

[1]  Wei Xing Zheng,et al.  Unified Stability Criteria of Random Nonlinear Time-Varying Impulsive Switched Systems , 2020, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Shengyuan Xu,et al.  Admissibility and stabilization of stochastic singular Markovian jump systems with time delays , 2018, Syst. Control. Lett..

[3]  Peng Shi,et al.  Backstepping Control in Vector Form for Stochastic Hamiltonian Systems , 2012, SIAM J. Control. Optim..

[4]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[5]  Jianwei Xia,et al.  Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters , 2020, Neural Networks.

[6]  Wenhai Qi,et al.  Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Shengyuan Xu,et al.  New insight into reachable set estimation for uncertain singular time-delay systems , 2018, Appl. Math. Comput..

[8]  Hidekazu Yoshioka,et al.  Unique solvability of a singular stochastic control model for population management , 2018, Syst. Control. Lett..

[9]  Qingling Zhang,et al.  Sliding mode control for T–S fuzzy singular semi-Markovian jump system , 2018, Nonlinear Analysis: Hybrid Systems.

[10]  Zhiwei Gao,et al.  Observer-based controller design for stochastic descriptor systems with Brownian motions , 2013, Autom..

[11]  Yunliang Wei,et al.  Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays , 2018, Appl. Math. Comput..

[12]  Qingling Zhang,et al.  Robust observer-based finite-time H∞ control for discrete-time singular Markovian jumping system with time delay and actuator saturation , 2018 .

[13]  Yang Wang,et al.  Weighted $${\mathcal {H}}_{\infty }$$H∞ consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies , 2019, Nonlinear Dynamics.

[14]  Yong Ren,et al.  Quantized Finite-Time Non-fragile Filtering for Singular Markovian Jump Systems with Intermittent Measurements , 2019, Circuits Syst. Signal Process..

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

[16]  Shen Cong,et al.  On almost sure stability conditions of linear switching stochastic differential systems , 2016 .

[17]  Weihai Zhang,et al.  Finite-Time Stability and Stabilization of Itô Stochastic Systems With Markovian Switching: Mode-Dependent Parameter Approach , 2015, IEEE Transactions on Automatic Control.

[18]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .

[19]  Yijie Peng,et al.  Efficient Learning for Selecting Important Nodes in Random Network , 2021, IEEE Transactions on Automatic Control.

[20]  Qingling Zhang,et al.  $$H_\infty $$H∞ filtering for stochastic singular fuzzy systems with time-varying delay , 2015 .

[21]  M. Fragoso,et al.  Continuous-Time Markov Jump Linear Systems , 2012 .

[22]  Xuerong Mao,et al.  Stability of Singular Stochastic Systems With Markovian Switching , 2011, IEEE Transactions on Automatic Control.

[23]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for singular systems , 2007, Syst. Control. Lett..

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

[25]  Hamid Reza Karimi,et al.  $\mathscr {L}_\infty$ Control for Positive Delay Systems With Semi-Markov Process and Application to a Communication Network Model , 2019, IEEE Transactions on Industrial Electronics.

[26]  Patrizio Colaneri,et al.  Mean square stability of linear systems with Poisson jumps , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[27]  S. Zhong,et al.  Asymptotic stability in probability of singular stochastic systems with Markovian switchings , 2017 .

[28]  Guanghui Wen,et al.  H∞ control for uncertain switched nonlinear singular systems with time delay , 2013 .

[29]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[30]  Shengyuan Xu,et al.  Reliable exponential H∞ filtering for singular Markovian jump systems with time‐varying delays and sensor failures , 2018, International Journal of Robust and Nonlinear Control.

[31]  R. Serfozo.  Basics of Applied Stochastic Processes , 2012 .

[32]  Yen-Chen Liu,et al.  Hybrid-triggered reliable dissipative control for singular networked cascade control systems with cyber-attacks , 2020, J. Frankl. Inst..

[33]  Yuqiang Wu,et al.  A design scheme of variable structure H-infinity control for uncertain singular Markov switched systems based on linear matrix inequality method , 2007 .

[34]  Frank L. Lewis,et al.  Cooperative Output Regulation of Singular Heterogeneous Multiagent Systems , 2016, IEEE Transactions on Cybernetics.

[35]  Weihai Zhang,et al.  New results on stability of singular stochastic Markov jump systems with state‐dependent noise , 2015, 1509.01102.

[36]  Weihai Zhang,et al.  A unified framework for asymptotic and transient behavior of linear stochastic systems , 2018, Appl. Math. Comput..

[37]  Li Sheng,et al.  Some remarks on stability of stochastic singular systems with state-dependent noise , 2015, Autom..

[38]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Nam Kyu Kwon,et al.  Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates , 2019, Nonlinear Dynamics.

[40]  H. Karimi,et al.  ℒ₁ Control of Positive Semi-Markov Jump Systems With State Delay , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[41]  Hao Shen,et al.  Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals , 2018, Studies in Systems, Decision and Control.

[42]  Shengyuan Xu,et al.  Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation , 2021, IEEE Transactions on Automatic Control.

[43]  Shengyuan Xu,et al.  Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations , 2018, IEEE Transactions on Automatic Control.

[44]  Victor Sreeram,et al.  Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters , 2018, IEEE Transactions on Fuzzy Systems.

[45]  Qingling Zhang,et al.  Analysis and Design of Singular Markovian Jump Systems , 2014 .

[46]  Lei Zhou,et al.  Stability analysis of switched linear singular systems , 2013, Autom..

[47]  Weihai Zhang,et al.  Finite‐time guaranteed cost control for Itô Stochastic Markovian jump systems with incomplete transition rates , 2017 .

[48]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.