An algorithm for estimating the stability domain of linear discrete-time systems with saturations

The aim of this paper is to propose a simple algorithm allowing determination of some positively invariant and asymptotically stable domains of nonlinear behaviours for linear state feedback discrete-time systems with saturation. Some theoretical results are given and used as support for the proposed approach which can be considered as a complement to methods based on the theory of linear systems with states and control constraints. The resulting algorithm basically consists of testing the decrease of a known Lyapunov function at vertices of a convex polyhedron of matrices