Differential linear matrix inequality in optimal sampled-data control

Abstract

This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a convex programming problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic programming equation associated to the time interval corresponding to two successive sampling instants. The design problems to be dealt with are convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.