Reachable set estimation of singular semi-Markov jump systems

Abstract This work is concerned with the problem of reachable set estimation for a class of singular semi-Markov jump system with time-varying delay under zero initial condition. Firstly, the technique of linear matrix inequality and two different methods are used to deal with the uncertain transition rate. Secondly, the boundary technique is applied to the fast subsystem without any assumptions about the system matrix. Finally, the reachable set mean-square bounded conditions for singular semi-Markov jump system with time-varying delay are given. The numerical simulation verifies the correctness of the theoretical analysis.

[1]  Jianxun Li,et al.  Optimal Filtering and a Smoothing Algorithm for a Singular System With a Complex Stochastic Uncertain Parameter Matrix , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  James Lam,et al.  On reachable set estimation of singular systems , 2015, Autom..

[3]  Jong-Tae Lim,et al.  Stabilization of Approximately Feedback Linearizable Systems Using Singular Perturbation , 2008, IEEE Transactions on Automatic Control.

[4]  Jiemei Zhao,et al.  Algebraic criteria for reachable set estimation of delayed memristive neural networks , 2019, IET Control Theory & Applications.

[5]  Hamid Reza Karimi,et al.  H∞ control of Markov jump time-delay systems under asynchronous controller and quantizer , 2019, Autom..

[6]  Guangdeng Zong,et al.  Adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with actuator faults , 2021, Int. J. Syst. Sci..

[7]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[8]  Dong Yang,et al.  Decentralized Adaptive Command Filtered Neural Tracking Control of Large-Scale Nonlinear Systems: An Almost Fast Finite-Time Framework , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Jun Shen,et al.  Stability Analysis for Positive Singular Systems With Time-Varying Delays , 2018, IEEE Transactions on Automatic Control.

[10]  Fuad E. Alsaadi,et al.  Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems , 2019, International Journal of Adaptive Control and Signal Processing.

[11]  Kun Liu,et al.  Comparison of bounding methods for stability analysis of systems with time-varying delays , 2017, J. Frankl. Inst..

[12]  F. Lewis.  A survey of linear singular systems , 1986 .

[13]  Baoping Jiang,et al.  Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations , 2015, Appl. Math. Comput..

[14]  Min Wu,et al.  Delay-dependent robust load frequency control for time delay power systems , 2013, 2013 IEEE Power & Energy Society General Meeting.

[15]  Jinde Cao,et al.  Reliable Event-Triggered Asynchronous Extended Passive Control for Semi-Markov Jump Fuzzy Systems and Its Application , 2020, IEEE Transactions on Fuzzy Systems.

[16]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[17]  Liang Ye,et al.  Stabilization of a class of fuzzy stochastic jump systems with partial information on jump and sojourn parameters , 2020 .

[18]  Lei Zhou,et al.  Stabilization of switched linear singular systems with state reset , 2019, J. Frankl. Inst..

[19]  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.

[20]  Shouming Zhong,et al.  Triple integral approach to reachable set bounding for linear singular systems with time‐varying delay , 2017 .

[21]  Peng Shi,et al.  Sliding Mode Control of Singular Stochastic Markov Jump Systems , 2017, IEEE Transactions on Automatic Control.

[22]  Peng Shi,et al.  Model Reduction of Markovian Jump Systems With Uncertain Probabilities , 2020, IEEE Transactions on Automatic Control.

[23]  Shengyuan Xu,et al.  Reachable set estimation for discrete‐time linear systems with time delays , 2015 .

[24]  Wenhai Qi,et al.  Almost fast finite‐time adaptive tracking control for a class of full‐state constrained pure‐feedback nonlinear systems , 2020, International Journal of Robust and Nonlinear Control.

[25]  El-Kébir Boukas,et al.  Control of Singular Systems with Random Abrupt Changes , 2008 .

[26]  Qingling Zhang,et al.  Passivity and Optimal Control of Descriptor Biological Complex Systems , 2008, IEEE Transactions on Automatic Control.

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

[28]  James Lam,et al.  Estimation and synthesis of reachable set for switched linear systems , 2016, Autom..

[29]  Wei Xing Zheng,et al.  Adaptive Event-Triggered SMC for Stochastic Switching Systems With Semi-Markov Process and Application to Boost Converter Circuit Model , 2021, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Emilia Fridman,et al.  On reachable sets for linear systems with delay and bounded peak inputs , 2003, Autom..

[31]  Zheng-Guang Wu,et al.  Observer-Based Sliding Mode Control for Markov Jump Systems With Actuator Failures and Asynchronous Modes , 2021, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  Hieu Minh Trinh,et al.  Exponential stability of time-delay systems via new weighted integral inequalities , 2015, Appl. Math. Comput..

[33]  Choon Ki Ahn,et al.  Reachable set estimation for Takagi-Sugeno fuzzy systems against unknown output delays with application to tracking control of AUVs. , 2018, ISA transactions.

[34]  Fuad E. Alsaadi,et al.  Adaptive Neural-Network-Based Dynamic Surface Control for Stochastic Interconnected Nonlinear Nonstrict-Feedback Systems With Dead Zone , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[35]  Jiemei Zhao,et al.  A new result on reachable set estimation for time‐varying delay singular systems , 2020, International Journal of Robust and Nonlinear Control.

[36]  Xuan Li,et al.  Exponential synchronization of switched genetic oscillators with time-varying delays , 2014, J. Frankl. Inst..

[37]  Yang Shi,et al.  Stabilization of non-homogeneous hidden semi-Markov Jump systems with limited sojourn-time information , 2020, Autom..

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

[39]  Lydia Tapia,et al.  Hybrid Dynamic Moving Obstacle Avoidance Using a Stochastic Reachable Set-Based Potential Field , 2017, IEEE Transactions on Robotics.

[40]  Mykel J. Kochenderfer,et al.  A Reachability Method for Verifying Dynamical Systems with Deep Neural Network Controllers , 2019, ArXiv.

[41]  Xian Zhang,et al.  A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay , 2012 .

[42]  Zhiguang Feng,et al.  Reachable set estimation for neutral Markovian jump systems with mode‐dependent time‐varying delays , 2020, Optimal Control Applications and Methods.

[43]  Jimin Wang,et al.  Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems , 2016, Appl. Math. Comput..

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

[45]  Zhiguang Feng,et al.  Reachable set synthesis of singular Markovian jump systems , 2020, J. Frankl. Inst..

[46]  Yajuan Liu,et al.  Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique , 2021, Appl. Math. Comput..

[47]  Weiming Xiang,et al.  Output Reachable Set Estimation and Verification for Multilayer Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[48]  Hui Liu,et al.  Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems , 2018, Complex..

[49]  Lei Zhou,et al.  New Results on Stability Analysis of Markovian Switching Singular Systems , 2019, IEEE Transactions on Automatic Control.

[50]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[51]  Zheng-Guang Wu,et al.  Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays , 2017, IEEE Transactions on Cybernetics.

[52]  Zhang Baoyong,et al.  New results on reachable set estimation for singular systems with time-varying delays , 2017, 2017 36th Chinese Control Conference (CCC).

[53]  Hiroaki Mukaidani,et al.  Nash games for multiparameter singularly perturbed systems with uncertain small singular perturbation parameters , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[54]  Liang Zhang,et al.  Improved results on reachable set estimation of singular systems , 2020, Appl. Math. Comput..

[55]  Jin-Hoon Kim,et al.  Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances , 2008, Autom..