Stabilizing composite control for systems modeled by singularly perturbed Itô differential equations with two small time constants

In this paper, we discuss the stabilizing composite control design for a class of multiparameter singularly perturbed systems governed by Itô differential equations. The asymptotic stability in mean square (ASMS) of the closed-loop system is addressed. First, the asymptotic structure of solutions of suitable Lyapunov type equation via multimodeling analysis is established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled algebraic linear equations which define a resolvent positive operator. Moreover, it is noteworthy that this is the first time conditions for the existence of the stabilizing feedback gain. These conditions are expressed in terms of solvability of a system of linear matrix inequalities. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided.