Control Design Based on Generalized Lur'e Lyapunov Functions for Sampled‐Data Lur'e Systems

This article addresses the synthesis of stabilizing control laws for aperiodic sampled‐data Lur'e systems. Based on a hybrid system representation of the closed‐loop system and a timer‐dependent generalized Lur'e–Postnikov type Lyapunov function, stabilization conditions are obtained by separating decision variables with the application of two instances of Finsler's lemma. To overcome the nonconvexity of these conditions, the controller parameters are obtained from an iterative procedure with guaranteed feasible solutions at each iteration. Controller gains are computed with the goal of maximizing the intersampling interval or the sector where the nonlinearity lies, while ensuring that the origin of the closed‐loop system is globally asymptotically stable.