Robust Static Output Feedback H∞ Control of Linear Discrete-Time Polytopic Systems Using a New Synthesis Condition with Reduced Conservatism

This paper presents a novel approach for the synthesis of robust static output feedback {H } controllers for linear discrete-time systems subject to polytopic uncertainties and external disturbances. By employing a parameter-dependent Lyapunov function combined with bounding matrix inequalities, we derive sufficient bilinear matrix inequality (BMI) conditions for controller synthesis. To address the inherent nonconvexity of the BMIs, the cone complementarity technique is utilized, resulting in a tractable linear matrix inequality (LMI) -based formulation. Numerical examples illustrate that the proposed method achieves reduced conservatism in disturbance attenuation compared to existing approaches. The proposed framework offers an effective and practical solution for robust static output feedback H∞ control of uncertain discrete-time systems.