Robust observer-based stabilization of linear systems with parametric uncertainties: Comparisons and suggested improvements

This paper addresses the problem of robust stabilization of continuous-time linear systems subject to norm-bounded parametric uncertainties via an observer-based feedback controller. The design of such controller is achieved through the Linear Matrix Inequality (LMI) techniques. A state of the art review for the synthesis of LMI-based stabilization conditions for uncertain linear continuous-time systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Analytical comparisons are provided to illustrate the favor from one method to another one. The comparison is achieved with respect to the conservatism injected into the LMI conditions. Then, our contribution in this work is to propose an enhanced design methodology of the robust observer-based controller. Our major objective is to show how a robust observer-based control law can be formulated to stabilize uncertain continuous-time linear systems and, at the same time, maximize the bounds on the parametric uncertainties which the system can tolerate without going unstable.