Feedback control of nonstandard discrete singularly perturbed system

Abstract

Feedback control of linear shift-invariant singularly perturbed discrete systems of the form x1(k+1) = (I+A11)x1(k) + A12)x2(k) + B1u(k), x2(k+1) = A21x1(k) + A22x2(k) + B2u(k), where (I-A22) may be singular is considered. Almost all available results are for the case of standard [1] systems, where (I-A22) is assumed to be nonsingular. In a recent result Khalil [2], showed that under stabilizability-detectability assumption on the slow and fast models, the theory of feedback control of singularly perturbed systems may be extended to the nonstandard case. In this paper we extend the idea of [2] to the case of discrete singularly perturbed systems under the same assumption