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

The focus of this chapter is the stabilizationStabilization of linear systemsLinearsystems under saturating aperiodic sampled-dataSampled-data control. By employing a hybrid systemHybridsystem representation, we establish conditions for the local and global stabilityGlobal stability of the origin of the closed-loop system using a specific class of quadratic timerLyapunovtimer dependent Lyapunov function (clock) dependent Lyapunov functionsLyapunovfunction. 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 AttractionRegion 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.