Design of Saturating Aperiodic Sampled-data Control Laws for Linear Plants: a Hybrid System Approach

This work addresses the problem of stabilization of linear systems under saturating aperiodic sampled-data control. Considering an impulsive model, a hybrid system formalism is applied to obtain local stability conditions for the origin of the closed-loop system. Thus, considering the class of quadratic clock (timer) dependent Lyapunov function candidates, conditions in the form of matrix inequalities are proposed to design the parameters of the control law. An LMI-based optimization problem aiming at computing the control law to maximize an estimate of the region of attraction of the origin (RAO) is therefore proposed.