Robust guaranteed cost control for uncertain discrete-time systems with state and input quantizations

Abstract

The robust guaranteed cost control problem for uncertain discrete-time systems with state and input quantizations has been studied in this paper. The polytope type uncertainties are considered in the plants. Different from previous related works, a novel guaranteed cost control strategy has been put forward in this paper. The novelty and challenge lie in that the quantized state and quantized input are included in the guaranteed cost function. Through introducing some auxiliary scalars and combining with the S-procedure, new criteria are developed for the robust stability and guaranteed cost performance for discrete-time systems with state and input quantizations. Based on a new two-step design strategy, the controller and dynamic quantizers can be easily obtained by means of linear matrix inequalities. In the end, two examples are given to demonstrate the effectiveness and applicability of the proposed method.