Leakage Delays in T–S Fuzzy Cellular Neural Networks

Abstract

In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for cellular neural networks (CNNs) with mixed time-varying delays and time delay in the leakage term via the delay decomposition approach. First, a sufficient condition is given to ensure the existence and uniqueness of equilibrium point by using topological degree theory. Then, we present global asymptotic stability of equilibrium point by using linear matrix inequality (LMI) approach and by constructing an augmented LyapunovKrasovskii functional (ALKF) together with convex combination method. The proposed results can be easily solved by some standard numerical packages. Finally, four numerical examples are given to demonstrate the effectiveness and conservativeness of our proposed results.

Design of state estimator for bidirectional associative memory neural networks with leakage delays

“…The objective is to estimate the state of BAM neural network (1) from the available network outputs (2). Now the fullorder state estimation for the delayed BAM neural network (1) is designed as follows:…”

“…Park et al [24] investigated the synchronization problem for coupled neural networks with interval time-varying delays and leakage delay. The stability analysis of Takagi-Sugeno fuzzy cellular neural networks with mixed time-varying delays and time delay in the leakage term via the delay decomposition approach has been carried out in [2]. More recently, Liu [21] studied the existence and stability results for general bidirectional associative memory neural networks with time-varying delays in the leakage terms by using the fixed point theorem and Lyapunov technique.…”

Stability Analysis for Stochastic Markovian Jumping Neural Networks with Leakage Delay

“…However, the leakage delay studied above was constant. Subsequently, the research on leakage delay was extended to time-varying [14,15]. In [14], with Lyapunov method, a triple Lyapunov-Krasovskii functional term was employed to study the robust stability of discrete-time uncertain neural networks with leakage time-varying delay.…”

Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales

“…Such time delays in the leakage term are difficult to handle but has great impact on the dynamical behavior of neural networks. Therefore, it is meaningful to consider neural networks with time delays in the leakage terms ( [23,24,[27][28][29][30][31]). On the other hand, the neural networks are often subject to abrupt changes at certain moments due to instantaneous perturbations which lead to impulsive effects.…”