New results on stability criteria for neural networks with time-varying delays

Abstract

In this paper, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new augmented Lyapunov-Krasovskii's functional and some novel analysis techniques, improved delaydependent criteria for checking the stability of the neural networks are established. The proposed criteria are presented in terms of linear matrix inequalities (LMIs) which can be easily solved and checked by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.

Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions

“…Theorem 1 There exist (αβ ) n equilibria for system (1) with activation function (2), if the following conditions hold,…”

“…(13). Then,z =x + iȳ is a unique equilibrium point of system (1) in Ω . Due to the arbitrariness of Ω and ε, there exist (αβ ) n equilibria in C n , which locate in each subregion of Φ.…”

“…Therefore, activation functions have an important influence for the existence of multiple equilibria. Next, we investigate the stability of multiple equilibria for system (1) with activation function (2).…”

“…. Since the real part and imaginary part of activation function (2) have individual properties, we can separate system (1) into its real and imaginary parts. By separating the state, the connection weight, the activation function, and the external input, we get a real part x i (t) and an imaginary part y i (t) for z i (t), respectively; a R i j and a I i j are the real part and imaginary part of a i j , respectively; b R i j and b I i j are the real part and imaginary part of b i j , respectively; u R i and u I i are the real part and imaginary part of u i , respectively.…”

“…In the past few decades, recurrent neural networks with their various generalizations have been extensively investigated due to their potential applications in pattern classification, associative memory, reconstruction of moving images, signal processing, parallel computation, and solving some classes of optimization problems. [1][2][3][4][5] Associative memories are brain-style devices, which are designed to memorize a set of patterns such that the stored patterns can be retrieved with the initial probes containing sufficient information about the patterns. In the associative memory based on recurrent neural networks, the stable output vectors are designed as the desired patterns.…”