An LMI Approach to Guaranteed Cost Control of Stochastic Linear Time-Delay Systems

Abstract

For stochastic linear time-delay systems with a given quadratic cost function, the guaranteed cost control problem, by state feedback controllers, was studied by introducing Lyapunov functional, using Ito lemma, Schur complement lemma and stochastic analysis methods. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities. And then the optimal guaranteed cost control law which minimizes the guaranteed cost of the stochastic linear closed-loop time-delay systems is also formulated.