Optimal Sampled–Data State Feedback Control of Linear Systems ⋆

This paper addresses and solves two optimal state-feedback control design problems for sampled-data systems. First, we reformulate the closed-loop system as a special linear hybrid system. Then, two theorems are developed to evaluate the H2 and the H∞ performances of hybrid systems using specific two-point boundary value problems. Both theorems are adapted to provide optimal control conditions, based on linear matrix inequalities (LMIs), for the statefeedback problems under consideration. These results are generalised to cope with non-uniform data-rates in the communication channel between the controller and the plant.