Reducing conservatism of extended linear matrix inequality condition for discrete‐time static output feedback controller design

Abstract This paper proposes a method to design static output feedback controllers for linear discrete‐time systems. The proposed approach provides formulations to solve stabilization, H 2 and H ∞ control problems with reduced conservatism by the extended linear matrix inequality (LMI) conditions. By introducing auxiliary decision variables into the extended LMIs, necessary and sufficient conditions for each control problem with static output feedback are derived. When these auxiliary decision variables are fixed as constant matrices, the conditions can be treated as LMIs. We also propose iterative algorithms to obtain one of the auxiliary decision variables for the stabilization problem, as well as iterative algorithms to optimize auxiliary decision variables for the H 2 and H ∞ control problems. Numerical design examples illustrate that the proposed method increases the probability of finding a static output feedback gain compared to the original extended LMI condition. Furthermore, it is also shown that H 2 and H ∞ control performances can be optimized through iterative LMI calculations, achieving better control performances compared to the original extended LMI conditions.