Descriptor Formulation for a Robust Static Output Feedback H<Sub>∞</Sub> Control for Polytopic Discrete-Time System

This paper investigates the problem of robust static output feedback (SOF) H-infinity controllers for polytopic uncertain discrete-time systems. The descriptor redundancy approach and linear matrix inequality (LMI) techniques are applied to solve the static output feedback H-infinity controllers problem. By considering auxiliary slack variables with free structure, new sufficient conditions for static output feedback H-infinity design are presented in terms of linear matrix inequalities (LMIs), which guarantee the robust stability of the closed-loop systems under prescribed H-infinity performances. Numerical examples are given to illustrate the advantages of the proposed procedure when compared with other methods available in the literature.