Stabilization of discrete-time switched singular systems with state, output and switching delays

Abstract This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

[1]  Joaquín Collado,et al.  Exponential estimates for neutral time-delay systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

[2]  Patrizio Colaneri,et al.  Stability and Stabilization of Continuous-Time Switched Linear Systems , 2006, SIAM J. Control. Optim..

[3]  Asier Ibeas,et al.  On singular hybrid switched and impulsive systems , 2018 .

[4]  H. Karimi,et al.  Robust H∞ reliable control for delta operator switched systems with time-varying delays under asynchronous switching , 2015 .

[5]  Shengyuan Xu,et al.  Stabilization of discrete-time singular systems: a matrix inequalities approach , 1999, Autom..

[6]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[7]  Hai Lin,et al.  On l1 stability of switched positive singular systems with time‐varying delay , 2017 .

[8]  Asier Ibeas,et al.  Switched nonlinear singular systems with time‐delay: Stability analysis , 2015 .

[9]  Xiaolong Zheng,et al.  New Stability and Stabilization Conditions of Switched Systems with Mode-Dependent Average Dwell Time , 2017, Circuits Syst. Signal Process..

[10]  Jianghai Hu,et al.  Resilient Stabilization of Switched Linear Control Systems Against Adversarial Switching , 2017, IEEE Transactions on Automatic Control.

[11]  Jian Liang Wang,et al.  Delay-dependent exponential H-infinity filtering for discrete-time switched delay systems , 2012 .

[12]  Guangdeng Zong,et al.  Asynchronous finite-time dynamic output feedback control for switched time-delay systems with non-linear disturbances , 2016 .

[13]  Xi-Ming Sun,et al.  Lyapunov-Krasovskii functionals for switched nonlinear input delay systems under asynchronous switching , 2015, Autom..

[14]  Lei Liu,et al.  Stability Analysis and Delay Control for Switched Positive Linear Systems , 2018, IEEE Transactions on Automatic Control.

[15]  Kristi A. Morgansen,et al.  Stability of Time-Delay Feedback Switched Linear Systems , 2010, IEEE Transactions on Automatic Control.

[16]  E. Boukas,et al.  Stability and stabilization of discrete‐time singular Markov jump systems with time‐varying delay , 2010 .

[17]  Myeong-Jin Park,et al.  Augmented Lyapunov-Krasovskii Functional Approach to Stability of Discrete Systems With Time-Varying Delays , 2017, IEEE Access.

[18]  Piyapong Niamsup,et al.  Finite-time stability of singular nonlinear switched time-delay systems: A singular value decomposition approach , 2017, J. Frankl. Inst..

[19]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

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

[21]  Zhifeng Gao,et al.  Stabilization of discrete-time switched singular time-delay systems under asynchronous switching , 2012, J. Frankl. Inst..

[22]  Peng Shi,et al.  Delay-dependent exponential H ∞ filtering for discrete-time switched delay systems: H ∞ FILTERING FOR DISCRETE-TIME SWITCHED DELAY SYSTEMS , 2012 .

[23]  Asier Ibeas,et al.  Exponential stability of hybrid switched nonlinear singular systems with time-varying delay , 2013, J. Frankl. Inst..

[24]  Ahmad Haidar,et al.  Exponential stability of singular systems with multiple time-varying delays , 2009, Autom..

[25]  Bing Chu,et al.  Stabilization of switched nonlinear differential algebraic systems and application to power systems with OLTC , 2011, Proceedings of the 30th Chinese Control Conference.

[26]  Caiyun Wu,et al.  Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching , 2017, J. Frankl. Inst..

[27]  Paul I. Barton,et al.  Nonsmooth differential-algebraic equations in chemical engineering , 2017, Comput. Chem. Eng..

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

[29]  Weiming Xiang,et al.  Mode-identifying time estimation and switching-delay tolerant control for switched systems: An elementary time unit approach , 2016, Autom..

[30]  Jun Zhao,et al.  Stabilization of networked switched linear systems: An asynchronous switching delay system approach , 2015, Syst. Control. Lett..

[31]  M. Shafiee,et al.  On the stability issues of switched singular time‐delay systems with slow switching based on average dwell‐time , 2014 .

[32]  Zhi-Gang Wu,et al.  Dynamic output feedback control for a class of switched delay systems under asynchronous switching , 2013, Inf. Sci..

[33]  Guangdeng Zong,et al.  Robustly resilient memory control for time-delay switched systems under asynchronous switching , 2017 .

[34]  Chengzhi Yuan,et al.  Hybrid Control for Switched Linear Systems With Average Dwell Time , 2015, IEEE Transactions on Automatic Control.

[35]  Peng Shi,et al.  Asynchronously switched control of a class of slowly switched linear systems , 2012, Syst. Control. Lett..

[36]  Jing Wang,et al.  Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback , 2018, Appl. Math. Comput..

[37]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[38]  Bart De Schutter,et al.  A novel Lyapunov function for a non-weighted L2 gain of asynchronously switched linear systems , 2018, Autom..

[39]  Guanghong Yang,et al.  Optimal partitioning method for stability analysis of continuous/discrete delay systems , 2015 .

[40]  Jing Wang,et al.  New delay-dependent bounded real lemmas of polytopic uncertain singular Markov jump systems with time delays , 2014, J. Frankl. Inst..

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

[42]  Jinxing Lin,et al.  Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach , 2013 .

[43]  Jong-Hae Kim,et al.  Delay-dependent robust Hinfinity filtering for uncertain discrete-time singular systems with interval time-varying delay , 2010, Autom..

[44]  Sophie Tarbouriech,et al.  Control co-design for discrete-time switched linear systems , 2017, Autom..

[45]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[46]  Yuechao Ma,et al.  Finite-time H∞ control for discrete-time switched singular time-delay systems subject to actuator saturation via static output feedback , 2016, Int. J. Syst. Sci..

[47]  Zhifeng Gao,et al.  Control discrete-time switched singular systems with state delays under asynchronous switching , 2013, Int. J. Syst. Sci..

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

[49]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.