Relaxed Stabilization and Disturbance Attenuation Control Synthesis Conditions for Polynomial Fuzzy Systems

This article presents both stabilization and disturbance attenuation control synthesis conditions for a class of polynomial fuzzy systems. The sum of squares conditions is relaxed by restricting the domain of the polynomial variables that represent the membership functions as well as by using the line integral polynomial fuzzy Lyapunov function. For the disturbance attenuation problem, we consider the transformation of the Hamilton-Jacobi-Isaacs equation into a set of inequalities and a policy iteration algorithm to approximate its value function. Furthermore, we propose an alternative path following to find the initial L-2 gain stabilizing control policy. Five examples are provided to demonstrate the effectiveness of the proposed conditions.

Automated summary

This article presents synthesis conditions for both stabilization and disturbance attenuation control for a class of polynomial fuzzy systems. It relaxes the sum of squares conditions by restricting the domain of the polynomial variables representing the membership functions and using a line integral polynomial fuzzy Lyapunov function. Additionally, it addresses the disturbance attenuation problem by transforming the Hamilton-Jacobi-Isaacs equation into a set of inequalities and using a policy iteration algorithm to approximate its value function. Furthermore, an alternative path following method is proposed to find the initial L-2 gain stabilizing control policy.