Stabilisation of polytopic singularly perturbed linear systems

This article deals with two time-scale polytopic linear systems in the singular perturbation form and in discrete-time. The aim is to propose well-conditioned convex conditions for stability analysis and control design. As the classical LTI time-scale separation-based approach is not successful in the case of polytopic singularly perturbed systems, our method leads to linear matrix inequality conditions independent of the singular perturbation parameter and offers an interesting solution from a numerical point of view. In addition, the conservatism of the proposed approach is limited as it is based on parameter-dependent Lyapunov functions. A numerical example taken from the literature illustrates the effectiveness of the given stabilisation conditions.