Optimal guaranteed cost control of linear uncertain systems: LMI approach

Abstract

Abstract In this paper, we study the guaranteed cost control problem for a class of linear systems with norm-bounded time-varying parameter uncertainty and a quadratic cost function in a linear matrix inequality (LMI) framework. The solvability condition is expressed as a system of LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of guaranteed cost controllers. The LMI-based characterization of guaranteed cost controllers enables us to easily solve the guaranteed cost control problem with some additional requirements. As a result we directly handle the optimal guaranteed cost control problem.