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LMI-based output feedback control of singularly perturbed systems with guaranteed cost

This paper addresses the problem of dynamic output feedback controller design for linear two time-scales dynamics. Unlike most of the works in the literature on singularly perturbed systems, we also consider the case where the state matrix of the fast dynamics is singular (nonstandard systems) and unstable. Our approach relies on decoupling the slow and fast dynamics of the closed-loop system and applying algebraic manipulations based on Finsler’s Lemma to obtain ε-dependent and ε-independent controllers. The design conditions are computationally oriented since they are expressed in term of Linear Matrix Inequalities (LMIs). On top of this, a quadratic cost is guaranteed to be upper-bounded for all positive values of the singular parameter. The proposed conditions circumvent some drawbacks of the existing works on this topic by providing a dynamic controller that does not depend on the singular parameter. A numerical example illustrates the effectiveness of the proposed approach.