Regional stability analysis of aperiodic sampled-data dynamic output feedback control systems under actuator saturation

This paper addresses the problem of local stability analysis of the connection between a continuous-time linear system with input saturation and a discrete-time output feedback controller updated aperiodically. To address the problem, we consider a hybrid system model to represent the closed-loop system dynamics. Using a quadratic timer-dependent Lyapunov function candidate and a generalized sector condition to deal with saturation effects, timer-dependent LMI conditions are formulated to certify the local stability of the origin and to provide estimates of its region of attraction. Considering a polynomial timer dependency, optimization problems based on semidefinite programming are proposed to maximize an estimate of the region of attraction of the origin or the upper bound of the possible variation of the sampling interval for which the stability is ensured, given a set of admissible initial conditions. A numerical example illustrates the application of the method and the conservatism reduction when compared to a previous approach.