Piecewise quadratic stability of fuzzy systems

TLDR

The paper proposes a new approach for stability analysis of fuzzy systems. The method uses continuous piecewise‑quadratic Lyapunov functions and gain‑scheduling to derive convex LMI‑based stability conditions, with computational efficiency improvements. Illustrative examples confirm that the proposed LMI‑based conditions outperform single quadratic Lyapunov function analysis.

Abstract

Presents an approach to stability analysis of fuzzy systems. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The approach exploits the gain-scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities. Examples demonstrate the many improvements over analysis based on a single quadratic Lyapunov function. Special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described.