Improved Synthesis of Saturating Sampled-Data Control Laws for Linear Plants

Arthur Scolari Fagundes, João Manoel Gomes da Silva Jr., Marc Jungers

Abstract: The focus of this chapter is the stabilization of linear systems under saturating aperiodic sampled-data control. By employing a hybrid system representation, we establish conditions for the local and global stability of the origin of the closed-loop system using a specific class of quadratic timer (clock) dependent Lyapunov functions. These conditions are formulated as Sum-of-Squares constraints within optimization problems, enabling the design of stabilizing control laws that aim to maximize an estimate of the Region of Attraction to the Origin (RAO) or to maximize the admissible interval between two sampling instants in order to ensure that a certain given set of initial conditions is included in the RAO.