Stability Analysis and Robust Controller Design for Uncertain Discrete-time Singularly Perturbed Systems

In this paper, the stability analysis and controller design for uncertain discretetime singularly perturbed system are investigated via a matrix inequality approach. In analysis, the stability condition under which the singularly perturbed system is quadratically stable for sufficiently small singular perturbation parameter is derived in the formulation of linear matrix inequality (LMI). In synthesis, the stabilization condition turns out to be in the formulation of nonlinear matrix inequality and is solved by the proposed heuristic two-stage procedure. The reduced controller is also developed using the similar approach. Finally, some numerical examples are used to demonstrate the effectiveness of the proposed analysis and design techniques.