Output feedback stabilization of Takagi-Sugeno fuzzy bilinear time-delay systems

This paper is concerned with stability analysis and output feedback control design of fuzzy bilinear systems with time-varying delay. First, we consider the stability of the closed-loop systems by assuming a special form of a fuzzy controller. A delay-dependent stability condition, which is less conservative than delay-independent one, is given in terms of linear matrix inequality (LMI). Based on such a stability condition, we propose a state feedback stabilizing control design for fuzzy bilinear systems with time-varying delays. Next, we consider a fuzzy observer design for the same class of systems, and propose an observer design based on another delay-dependent condition. Then, we show that state feedback stabilizing controller and observer make an output feedback stabilizing controller. Finally, we give a numerical example to illustrate our design procedures and to show the effectiveness of our approach.