Performance analysis for linear discrete-time systems subject to actuator saturation

This paper investigates performance analysis problem under a given feedback law for discrete-time linear systems subject to actuator saturation. Two performance measures, the estimation of domain of attraction and L2 performance, are considered by combining the saturation-dependent Lyapunov function method with Finsler´s Lemma. New and less conservative conditions in the enlarged space containing both the state and its time difference, allowing extra degree of freedom for various performance analysis, are proposed. Furthermore, based on these results, two important lemmas and two iterative LMI-based optimization algorithms are also developed to optimize the performance indexes respectively. Numerical examples illustrate that the proposed methods improve recent results on the same problems.