Stabilization analysis of single-input polynomial fuzzy systems using control Lyapunov functions
Radian Furqon, Ying-Jen Chen, Motoyasu Tanaka, Kazuo A. TANAKA, Hua O. Wang · 2014
This paper presents a novel method for stabilization analysis of the single-input polynomial fuzzy systems using a sum of squares (SOS) approach to construct control Lyapunov functions (CLFs) for the systems. First, we represent a nonlinear system as a polynomial fuzzy system. Then, sufficient conditions in SOS terms for a positive definite function to become a CLF is presented. We solve the sufficient conditions using SOS optimization technique to construct the CLF. Finally, after a CLF is constructed, the controller for the system is designed using Sontag's formula. To illustrate the validity of the proposed approach, a design example is provided.