Further Enhancement on Robust $H_{\infty }$ Control Design for Discrete-Time Singular Systems

This note deals with the robust H_∞ control design for uncertain discrete-time singular systems. Necessary and sufficient conditions for the admissibility for these systems are formulated in strict linear matrix inequalities (LMIs) formulation. Then both state feedback and static output feedback controllers are studied and robust necessary and sufficient design conditions are expressed in terms of strict bilinear matrix inequalities (BMIs). Robust H_∞ controllers are designed for uncertain singular systems including uncertainties on matrix E. LMI design conditions are also proposed. An illustrative example is provided to show the effectiveness of the proposed approach.