Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.