Output Feedback Control Synthesis for Positive Fuzzy Systems Using a Sequential Linear Programming Approach

This paper studies the robust output feedbackl1control for positive Takagi-Sugeno (T-S) fuzzy systems. A reduced-order dynamic output feedback (RODOF) controller is designed to preserve the positivity and stability of the closed-loop system while achieving anl1-induced performance. Sufficient conditions for satisfying mismatched multiple fuzzy summation inequalities and for the existence of RODOF controllers are first derived, which are formulated as a bilinear programming (BP) problem. To simultaneously address the bilinear and positivity constraints, an additional linear constraint is introduced to establish a linear approximation of the original non-convex constraint, by which we propose a sequential linear programming (SLP) algorithm to determine the desired controller parameters. Furthermore, by constructing an auxiliary stabilization problem and utilizing the convergence property of the SLP method, an initial feasible condition is systematically obtained, thus ensuring constraint satisfaction throughout the iterations. Finally, the feasibility and validity of the theoretical results are demonstrated by a tank system and a buck converter system.