SOS Stability Conditions for Nonlinear Systems Based on a Polynomial Fuzzy Lyapunov Function

摘要

In this paper, a new step on fuzzy relaxation for nonlinear systems' stability analysis is addressed. Inspired from non-quadratic Lyapunov functions (NQLF), regarding to quadratic ones (QLF), a new polynomial fuzzy Lyapunov function (PFLF) is proposed as an extension to the polynomial Lyapunov function (PLF) [22]. Following the latter post-LMI challenge, the obtained stability conditions are written in terms of a sum-of-squares (SOS) optimization problem. The proposed PFLF includes the well-studied NQLF ones as a special case. Moreover, the proposed SOS based stability conditions don't require unknown parameters as well as guarantee, when a solution exists, the global stability.