Guaranteed Cost Control for Uncertain Stochastic Systems with State and Input Delays

This paper deals with the problem of guaranteed cost control for uncertain stochastic systems with state and input-delays. Attention is focused on the design of a state feedback controller such that the resulting closed-loop system is mean-square asymptotically stable and guarantees that a given quadratic cost function has an upper bound. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of this problem is derived. When the LMI is satisfied, the expression of desired state feedback controller is proposed. A numerical example is given to demonstrate the feasibility of the proposed approach.

1. Introduction

In the past decades, considerable attention has been drawn to the problems of robust stability analysis and robust controller synthesis for linear state-space systems; see, e.g. [1]–[3]. In practical applications, however, we are concerned with constructing a control system which is not only stable but also ensures an adequate level of performance. This has motivated the study of guaranteed cost control problem, in which an upper bound on the closed-loop value of a quadratic cost function can be provided by using a fixed Lyapunov function. This technique has been found useful in certain applications. Recently, many researchers have considered the guaranteed cost control problem for uncertain systems with or without delays; see e.g. [4], [5].