Guaranteed Cost Control for Delayed Discrete-Time Linear Systems: A Lyapunov Matrix-Based Method

This paper is concerned with the guaranteed cost control problem for delayed discrete-time linear systems. Firstly, the concept of Lyapunov matrix is employed to construct a complete-type Lyapunov-Krasovskii functional. Secondly, solvable conditions of the problems under consideration are proposed. These conditions are formulated as several simple linear matrix inequalities, which can be solved by using the toolbox YALMIP of MATLAB. Thirdly, the precise form of the controller is proposed, which guarantees that the resultant closed-loop system is asymptotically stable and has a guaranteed cost. Finally, an example is given to illustrate the validity of the theoretical results.