Robust H-infinity Control of Linear Discrete-Time Systems with Uncertainties and Disturbances

Abstract

This paper presents an enhanced approach for synthesizing a robust static output feedback H-infinity controller for linear discrete-time systems with polytopic uncertainties and external disturbances. While this problem has been extensively studied in the literature, the proposed method distinguishes itself through the utilization of parameter-dependent Lyapunov functions and novel bounding techniques for bilinear terms. By employing a more flexible and accurate characterization of system dynamics and uncertainties, our approach achieves improved controller performance with less conservatism compared to existing methods. The formulation of the controller design problem involves converting the nonconvex optimization into a convex minimization one using a congruent transformation and the cone complementarity technique. This leads to a set of linear matrix inequality conditions that guarantee the existence of an effective robust output feedback H-infinity controller capable of mitigating the effects of uncertainties and disturbances on the system. Numerical simulations show that our proposed method outperforms existing results in terms of disturbance attenuation rates. © 2023 IEEE.