Robust Stabilization of Singularly Perturbed Systems with Uncertainties

Abstract

This paper considers the robust stabilization of singularly perturbed systems with time-varying unknowbut-bounded uncertainties. The H_∞ control method are used to establish the stability of the closed-loop system. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation with small parameter ε > 0. In order to overcome the computation difficulties caused by small parameter ε, we propose the ε-less quadratically stabilizing controller by using the results of the solution for above a algebraic Riccati equation. It is shown that if the reduced order Riccati equations have a positive definite stabilizing solution then the given uncertain linear system with the proposed controller independ of ε is quadraticaly stabilizable. To show the effectiveness of the proposed algorithm, numerical examples are included.