Abstract
This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.
Highlights
During the past decades, recurrent neural network (RNN) has been successfully applied in many fields, such as signal processing, pattern classification, associative memory design, and optimization
As the integration and communication delay is unavoidably encountered in implementation of RNN and is often the main source of instability and oscillations, much efforts have been expended on the problem of stability of RNNs with time delays
RNNs can be classified as local field networks and static neural networks based on the difference of basic variables [15]
Summary
Recurrent neural network (RNN) has been successfully applied in many fields, such as signal processing, pattern classification, associative memory design, and optimization. The stability of static recurrent neural networks (SRNNs) with timevarying delay was investigated in [16], where sufficient conditions were obtained guaranteeing the global asymptotic stability of the neural network. Some negative semi-definite terms were ignored in [16], which lead to the conservatism of the derived result. By retaining these terms and considering the low bound of the delay, some improved stability conditions were derived for SRNNs with interval time-varying delay in [17]. The problem of stability of SRNNs with timevarying delay is investigated based on the complete delaydecomposing approach [12]. If not explicitly stated, are assumed to have compatible dimensions
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