Abstract
This paper considers the quadratic stabilization of nonstandard singularly perturbed systems with uncer-tainties such that the so-called “matching conditions” are not satisfied. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation with small parameter ε<0. The main result in this paper is to propose a new recursive algorithm to solve the above equation and to find an ε independent sufficient conditions for the existence of the full-order stabilizing controller. One noteworthy advantage of the Riccati equation approach to obtaining a stablizing controller is that the uncertain matrix. A22+ΔA22(r22(t)) has unstable mode. Thus, our new results are applicable to both standard and nonstandard uncertain Singularly perturbed systems. To show the effectiveness of the proposed algorithm, numerical examples are included.
