LMI Conditions for Robust Stability of 2D Linear Discrete‐Time Systems

Abstract

Robust stability conditions are derived for uncertain 2D linear discrete‐time systems, described by Fornasini‐Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter‐dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.