Static Output Feedback ℋ_∞ and ℋ₂ Control for Discrete-time Linear Systems

This paper presents a novel methodology for the design of robust ℋ_∞ and ℋ₂ static output feedback (SOF) controllers for discrete-time linear systems. The proposed approach begins with the definition of an extended state feedback (ESF) controller and the formulation of a linear matrix inequality (LMI) condition for its design. Subsequently, an initial SOF control gain is derived using the ESF controller, followed by iterative LMI optimization to achieve a less conservative SOF controller. The effectiveness and superiority of the proposed method are demonstrated through comparative examples where existing methods either fail or produce more conservative results.