On the design of guaranteed cost controllers for a class of uncertain linear systems

Abstract

In this paper, we consider the guaranteed cost control problem (GCCP) for a class of uncertain linear systems with structured parametric uncertainty. We present an approach to the GCCP for systems with arbitrary rank uncertainty matrices based on a rank-one description of the uncertain linear system. A search for an adequate rank-one overbounding of the uncertainty matrices is included in an optimisation problem thus reducing the conservatism of previous methods based on rank-one description of the uncertain system. The paper extends previous results on the GCCP for a rank-one description of the uncertain system, an important description of uncertain systems. A feature of the proposed approach is that an upper bound on the guaranteed cost is minimized by solving an optimization problem with linear matrix inequalities. A numerical example is presented to illustrate the computational efficiency of the proposed approach. For comparison, we also include results for a polytopic description of the uncertain linear system.