Using linear matrix inequality for the guaranteed cost control with arbitrary rank uncertainty matrices

We consider the guaranteed cost control problem (GCCP) for systems with structured uncertainties. We present an approach to the GCCP for systems with arbitrary rank uncertainty matrices in which an upper bound for the cost is minimised by solving an optimisation problem with linear matrix inequalities (LMIs). The search for an adequate overbounding of the uncertainties is included in the optimisation problem thus avoiding an iterative search by trial and error. A numerical example is presented in order to illustrate the effectiveness of the proposed approach