Control Synthesis for Polynomial Fuzzy Systems Using Line-Integral Polynomial Fuzzy Lyapunov Function
Jairo Moreno Saenz, Motoyasu Tanaka, Kazuo A. TANAKA · 2018
In this paper, we present a generalization of the line-integral fuzzy Lyapunov function. Our proposal allows considering a conservative vector field of homogeneous polynomials in the consequent of the IF-THEN fuzzy rules, resulting in a line-integral polynomial fuzzy Lyapunov function. Based on the proposed Lyapunov function and using Positivstellensatz, we derive sum of squares nonconvex control synthesis conditions which are applicable to both Tagaki-Sugeno and polynomial fuzzy systems. Moreover, an initialization step for the path following iterative algorithm is proposed. Finally, the effectiveness of the relaxed conditions is demonstrated by two benchmark examples.