A note on stability and stabilization of discrete-time systems with time-varying delay

This paper is concerned with the stability and stabilization problem of the discrete-time systems with time-varying delay. Using “lifting” technique, a discrete-time system with time-varying delay is transformed into a switched system. On the basis of theories of switched systems, some necessary and sufficient stability conditions are obtained. However, these conditions are hard to check. Using the switched Lyapunov function approach, some equivalent sufficient stability conditions are developed. Based on these conditions, a state feedback controller with varying gains is designed. Numerical examples are given to show the effectiveness of the proposed method.

[1]  Yuanqing Xia,et al.  New stability and stabilization conditions for systems with time-delay , 2007, Int. J. Syst. Sci..

[2]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[3]  Silviu-Iulian Niculescu,et al.  Discretized Lyapunov functional for systems with distributed delay , 1999, 1999 European Control Conference (ECC).

[4]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[5]  J. Lam,et al.  IMPROVED CONDITIONS FOR DELAY‐DEPENDENT ROBUST STABILITY AND STABILIZATION OF UNCERTAIN DISCRETE TIME‐DELAY SYSTEMS , 2005 .

[6]  Dong Yue,et al.  A new state feedback H∞ control of networked control systems with time-varying network conditions , 2012, J. Frankl. Inst..

[7]  H. Unbehauen,et al.  Communique Robust H = observer design of linear state delayed systems with parametric uncertainty : the discrete-time case 1 , 1999 .

[8]  P. Bauer,et al.  A necessary and sufficient condition for robust asymptotic stability of time-variant discrete systems , 1993, IEEE Trans. Autom. Control..

[9]  Ho-Chan Kim,et al.  Hinfinity control of discrete-time linear systems with time-varying delays in state , 1999, Autom..

[10]  Guo-Ping Liu,et al.  NETWORKED PREDICTIVE CONTROL OF SYSTEMS WITH RANDOM COMMUNICATION DELAY , 2004 .

[11]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[12]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[13]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[14]  Hai Lin,et al.  Stabilization and performance analysis for a class of switched systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[16]  Jian Sun,et al.  Stability and stabilization for discrete systems with time-varying delays based on the average dwell-time method , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[17]  Senchun Chai,et al.  Design and stability analysis of networked control systems with random communication time delay using the modified MPC , 2006 .

[18]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[19]  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 .

[20]  Qing-Long Han,et al.  Delay-Dependent Robust $H_{\infty}$ Filtering for Uncertain Discrete-Time Systems With Time-Varying Delay Based on a Finite Sum Inequality , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[22]  Hai Lin,et al.  Persistent disturbance attenuation properties for networked control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[23]  M.L. Sichitiu,et al.  Stability of discrete time-variant linear delay systems and applications to network control , 2001, ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483).