Convex Optimization Approach to Observer-Based Stabilization of Uncertain Linear Systems

Abstract

New sufficient linear matrix inequality conditions guaranteeing the stability of uncertain linear systems by means of dynamic output feedbacks are presented. It is shown that the search of an observer-based controller for this class of systems is fundamentally decomposed into two main problems: robust stability with a memoryless state feedback and observer design with measured uncertainties. Under the fulfilment of the developed linear matrix inequalities conditions, we show that the observer-based problem is solvable without any need for some equality constraints or iterative computational algorithms. Examples showing the potential of the results are presented.