New condition for invariance of ellipsoidal sets for discrete-time saturated systems

In this paper, we consider the problem of characterizing the invariant and contractive ellipsoids for discrete-time saturated systems, as an estimate of the domain of attraction. The asymptotic stability of the controlled system is ensured by the contractive nature of the invariant set. Sufficient conditions for the existence of a quadratic set-induced Lyapunov function are established through the solution of a bilinear matrix inequalities (BMI) problem. Some computational considerations are analyzed to overcome the problem of complexity. An illustrative example is given to demonstrate the effectiveness of the proposed results, developed in this paper.