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Zbl 1198.34160
Rakkiyappan, R.; Balasubramaniam, P.
On exponential stability results for fuzzy impulsive neural networks. (English)
[J] Fuzzy Sets Syst. 161, No. 13, 1823-1835 (2010). ISSN 0165-0114

Summary: Complex nonlinear systems can be represented as a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy neural networks with impulsive effect and time-varying delays is investigated. The model for fuzzy impulsive neural networks with time-varying delays is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of impulsive neural networks with time-varying delays. Secondly, the exponential stability for fuzzy impulsive neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach. In addition, two numerical examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.

MSC 2000:: *34K20 Stability theory of functional-differential equations
92B20 General theory of neural networks
34K36
34K45 Equations with impulses

Keywords: exponential stability; fuzzy impulsive neural networks; generalized eigenvalue problem (GEVP); linear matrix inequality; Lyapunov-Krasovskii functional

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