DELAY DEPENDENT STOCHASTIC STABILITY AND APPLICATION IN CONTROL WITH LIMITED COMMUNICATION

Abstract A theorem by de Souza on stochastic stability of systems with delays has been strengthened. This result provides a condition for delay-dependent stability. As in many practical applications a realistic bound on the delay may be known such a result should be useful where simple delay-independent stability conditions fail. In particular, this has ramifications in the robustness of stability of systems controlled over finite capacity communication channels.

[1]  Robust stability and stabilization of deterministic and stochastic time-delay systems , 1997 .

[2]  Alexey S. Matveev The Instability of Optimal Control Problems to Time Delay , 2005, SIAM J. Control. Optim..

[3]  Erik I. Verriest,et al.  Stabilization of nonlinear stochastic systems with delay feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[4]  V. B. Kolmanovskii,et al.  MATRIX RICCATI EQUATIONS AND STABILITY OF STOCHASTIC LINEAR SYSTEMS WITH NONINCREASING DELAYS , 2004 .

[5]  Olivier Sename,et al.  Robust observer-controller for delay-differential systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  D. G. Korenevskii Stability with probability 1 of solutions of systems of linear ito stochastic differential-difference equations , 1987 .

[7]  C. D. Souza,et al.  Stability and stabilization of linear state-delayed systems with multiplicative noise* , 2000 .

[8]  M. Egerstedt,et al.  Control with delayed and limited information: a first look , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[10]  S. Mohammed Stochastic functional differential equations , 1984 .

[11]  Stability with probability 1 of solutions of systems of linear stochastic differential-difference Ito equations , 1991 .

[12]  Erik I. Verriest,et al.  Robust stability of time varying systems with unknown bounded delays , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[13]  Erik I. Verriest,et al.  Stability of stochastic systems with uncertain time delays , 1995 .

[14]  S. Niculescu,et al.  Stability analysis of time-delay systems : A lyapunov approach , 2006 .

[15]  Frank Kozin,et al.  A survey of stability of stochastic systems , 1969, Autom..

[16]  Erik I. Verriest Stabilization of deterministic and stochastic systems with uncertain time delays , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[17]  Erik I. Verriest Delay in state feedback control over a network , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).