Switched systems approach to state bounding for time delay systems

Abstract This paper investigates the problems of reachable set estimation for dynamic systems with time-varying delay and random delay. Different from the traditional Lyapunov-Krasovskii functional method, a switched systems approach is adopted to study the reachable set estimation problem for time-varying delay systems. Through augmentation, time-varying delay systems can be transformed into switched delay-free systems. The reachable set of a time-varying delay system is estimated based on its corresponding augmented switched system. The number of decision variables in the obtained reachable set estimation condition is small compared with the Lyapunov-Krasovskii functional method. In addition, the problem of mean square estimation of the system state for random delay systems is also studied. The effectiveness of the theoretical findings is verified through several simulation examples.

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

[2]  Daniel W. C. Ho,et al.  Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach , 2010, Autom..

[3]  J. Lam,et al.  Estimation and synthesis of reachable set for discrete‐time periodic systems , 2016 .

[4]  Hieu Minh Trinh,et al.  Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound , 2015, Appl. Math. Lett..

[5]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

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

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

[8]  J. Daafouz,et al.  Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems , 2008 .

[9]  D. Ho,et al.  Reachable set estimation for linear systems in the presence of both discrete and distributed delays , 2011 .

[10]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[11]  Wei Xing Zheng,et al.  On reachable set estimation of delay Markovian jump systems with partially known transition probabilities , 2016, J. Frankl. Inst..

[12]  Ju H. Park,et al.  On the reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances , 2011, Inf. Sci..

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

[14]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[15]  Le Van Hien,et al.  A novel approach to state bounding for discrete-time Markovian jump systems with interval time-varying delay , 2016, IMA J. Math. Control. Inf..

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

[17]  James Lam,et al.  Corrigendum to "On reachable sets for positive linear systems under constrained exogenous inputs" [Automatica 74 (2016) 230-237] , 2017, Autom..

[18]  Shengyuan Xu,et al.  Relaxed results on reachable set estimation of time‐delay systems with bounded peak inputs , 2016 .

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

[20]  Hieu Minh Trinh,et al.  Reachable sets bounding for switched systems with time-varying delay and bounded disturbances , 2017, Int. J. Syst. Sci..

[21]  Wim Michiels,et al.  Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach, Second Edition , 2014 .

[22]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .

[23]  Phan Thanh Nam,et al.  Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances , 2013, J. Optim. Theory Appl..

[24]  Weiming Xiang,et al.  Reachable set estimation and control for switched linear systems with dwell-time restriction , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[25]  Yin Sheng,et al.  Improved reachable set bounding for linear time-delay systems with disturbances , 2016, J. Frankl. Inst..

[26]  Pubudu N. Pathirana,et al.  Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays , 2011, Autom..