Robust Stabilization of Linear Systems with Delayed State and Control

Robust stabilization of linear systems with delays on both the state and control input is studied in this paper. Using an improved Lyapunov-Krasovskii functional, we establish new criteria that ensure the robust stability of the closed-loop system with memoryless state feedback controls. The generalized conditions are derived in terms of linear matrix inequalities (LMIs), allowing us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution and can be easily solved by numerical algorithms.

[1]  Vu Ngoc Phat,et al.  Global stabilization for linear continuous time-varying systems , 2006, Appl. Math. Comput..

[2]  Wei Xing Zheng,et al.  On improved robust stabilization of uncertain systems with unknown input delay , 2006, Autom..

[3]  F. Udwadia,et al.  Time delayed control of classically damped structural systems , 1994 .

[4]  Ju H. Park,et al.  Robust stabilization of uncertain systems with delays in control input: a matrix inequality approach , 2006, Appl. Math. Comput..

[5]  Dong Yue,et al.  Robust stabilization of uncertain systems with unknown input delay , 2004, Autom..

[6]  M. Corless,et al.  Bounded controllers for robust exponential convergence , 1993 .

[7]  Wook Hyun Kwon,et al.  Robust H ∞ Controller for State and Input Delayed Systems with Structured Uncertainties , 1997 .

[8]  Wook Hyun Kwon,et al.  Feedback stabilization of linear systems with delayed control , 1980 .

[9]  Wook Hyun Kwon,et al.  Robust stabilization of uncertain input-delayed systems using reduction method , 2001, Autom..

[10]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[11]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[12]  Firdaus E. Udwadia,et al.  Time‐delayed control design for active control of structures: principles and applications , 2007 .

[13]  Mohammad Hosseini,et al.  Time delayed control of structural systems , 2003 .

[14]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[15]  Firdaus E. Udwadia,et al.  Time-Delayed Positive Velocity Feedback Control Design for Active Control of Structures , 2006 .

[16]  Ethelbert Nwakuche Chukwu,et al.  Stability and Time-Optimal Control of Hereditary Systems - With Application to the Economic Dynamics of the US - - - - 2nd Edition , 2002, Series on Advances in Mathematics for Applied Sciences.

[17]  Vladimir Borisovich Kolmanovskiĭ,et al.  Control of Systems with Aftereffect , 1996 .

[18]  Z. Artstein.  Linear systems with delayed controls: A reduction , 1982 .

[19]  Sing Kiong Nguang,et al.  Robust H/sub /spl infin// control of a class of nonlinear systems with delayed state and control: a LMI approach , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[20]  V. Phat,et al.  Stabilization of Linear Nonautonomous Systems with Norm-Bounded Controls , 2006 .

[21]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..