Output feedback control for bilinear systems: a polytopic approach

Abstract

This paper deals with bilinear systems. A method is provided to design a bilinear dynamic output feedback controller aiming at two goals: first to ensure local exponential stability of the origin in the closed-loop form and second to determine an estimate of the basin of attraction of the origin as large as possible. We propose a bilinear term in the controller that acts as a counteraction to the influence of the bilinear term of the system. The design of a full-order controller is converted in a static output feedback problem of an augmented system and solved by sufficient conditions expressed as linear matrix inequalities (LMIs) by considering a polytopic approach. By describing the closed-loop system in a polytopic region of the state space, an algorithm is proposed to design a controller that maximizes the estimate of the domain of attraction and progressively increases the size of the polytope where the system is represented. The results are illustrated by a numerical example.