On LMI conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties

Abstract

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results.