New Criteria of Passivity Analysis for Fuzzy Time-Delay Systems With Parameter Uncertainties

• Published in: IEEE transactions on fuzzy systems Vol. 23; no. 6; pp. 2284 - 2301
• Main Authors: Wen, Shiping, Zeng, Zhigang, Huang, Tingwen, Yu, Xinghuo, Xiao, Mingqing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Delays; Fuzzy logic; Fuzzy systems; mixed delay; noise disturbance; Nonlinear systems; Passivity; Stochastic processes; Stochastic systems; time delay; Uncertain systems; Mixed delay; noise disturbance; time delay; passivity
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2015.2417913

This paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi-Sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, the parameter uncertainties, the stochastic disturbances, and nonlinearities are considered, where the parameter uncertainties enter into all the system matrices, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. By taking the relationship among the time delays, their lower and upper bounds into account, some less conservative linear-matrix-inequality-based delay-dependent passivity criteria are obtained without ignoring any useful terms in the derivative of Lyapunov functional. Finally, numerical examples are given to demonstrate the effectiveness and merits of the proposed methods.