Static output feedback control of polytopic systems using polynomial Lyapunov functions

This paper is concerned with the problem of robust static output feedback control design for continuous-time uncertain linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all system matrices. A two-stage linear matrix inequality procedure is proposed. At the first step, a stabilizing state feedback scheduled gain with polynomial or rational dependence on the parameters is determined. This state feedback gain is used as an input parameter for the second stage, which synthesizes the robust static output feedback gain. In both stages, a homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability. Numerical examples demonstrate that with the increase of the degree of the polynomial matrices more accurate results are obtained, outperforming the existing methods in the literature.