A BMI approach to guaranteed cost control of discrete-time uncertain system with both state and input delays

In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi‐definite optimization solver–PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method.