Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties

This paper studies the static output feedback (SOF) control problem of continuous-time linear systems with polytopic uncertainties. Novel LMI conditions with a line search over a scalar variable for designing robust SOF controllers are proposed, where the uncertain output matrix of the considered system is allowed to be not of full row rank. In particular, it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and Lyapunov matrix. Furthermore, the result is extended to the case of H∞H∞ control. Numerical examples are given to illustrate the effectiveness of the proposed method.