Zonotopic interval estimation for discrete-time Takagi–Sugeno fuzzy systems with a delayed nonquadratic framework

Abstract

This paper investigates the delayed nonquadratic zonotopic interval estimation for discrete-time Takagi–Sugeno (T-S) fuzzy systems. Due to the improvements made on traditional quadratic methods, the estimation accuracy is enhanced and the conservatism is efficiently reduced. Firstly, based on multiple sums and multisets of delays, an overall nonquadratic zonotopic estimation framework with tuneable delayed terms is proposed. A general observer gain computation method with L∞ performance is derived in terms of matrix inequalities shortly afterward. The design conditions are relaxed by selecting a group of specific multisets of delays that the observer gain acquisition problem is transformed into solving a set of linear matrix inequalities (LMIs). Furthermore, the rules for selecting appropriate multisets of delays, which limit the computational complexity and improve the design freedom, are analyzed. The feasibility, effectiveness, and practicability of the proposed method are illustrated by two examples finally.