Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1392.93038
Summary: This paper focuses on the globally exponential stability in Lagrange sense for Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg neural networks with time-varying delays. By employing Lyapunov method and delay inequality technique, we analyze two different types of activation functions which include both Lipschitz function and general activation functions, several easily verifiable sufficient criteria about linear matrix inequality form are obtained to guarantee the Lagrange exponential stability of Cohen-Grossberg neural networks with time varying delays which are represented by T-S fuzzy models. Meanwhile, the estimations of the globally exponentially attractive sets are given. Here, the existence and uniqueness of the equilibrium points need not be considered. Finally, two numerical examples with simulations are given to illustrate the effectiveness of the theoretical results.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K36 | Fuzzy functional-differential equations |
Keywords:
Cohen-Grossberg neural networks; Lagrange stability; Lyapunov function; time-varying delays; linear matrix inequality (LMI); T-S fuzzy modelReferences:
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