Design and analysis of LMI for stability and static output feedback control of discrete-time matrix sylvester system

This paper deals with the design of static output feedback (SOF) control for the discrete matrix sylvester system. The design principles of SOF formulation based on the linear matrix inequality (LMI) are expressed in terms of Bilinear Matrix Inequalities (BMIs). Non-convex stability conditions that emerge in the design of SOF control are to be transferred into convex stability conditions by using suitable techniques. This paper presents the results that are necessary to address the convexity problem. This paper also presents a novel approach for the transformation of BMI constraints into LMIs. The developed theory and established results are verified and validated by numerical simulations.