Membership-Function-Dependent Design of $L_1$-Gain Output-Feedback Controller for Stabilization of Positive Polynomial Fuzzy Systems

This article presents the $L_1$ -gain polynomial fuzzy output-feedback controller design and stability analysis using sum-of-squares (SOS) approach for positive fuzzy-model-based (PPFMB) control systems. The polynomials, positivity, optimal performance make some existing convex methods general systems inapplicable. To overcome this problem, first, an augmented system of PPFMB is constructed; then, by introducing constraint conditions mathematical techniques, nonconvex positivity are skillfully transformed into ones simultaneously. In addition, to flexibly lower implementation cost, imperfect premise matching concept taken account design. Besides, high-degree-polynomial approximation method adopted conduct incorporating information membership functions boundary state variables. On basis Lyapunov theory, relaxed in terms SOS form obtained. Finally, two simulation examples presented verify feasibility theoretical results.