Robust stochastic convergence and stability of neutral‐type neural networks with Markovian jump and mixed delays

Abstract

SummaryThe robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral‐type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay‐type inequality for stochastic differential equations, a delay‐dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay‐dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd.

Extended dissipative output‐feedback control for discrete‐time bidirectional associative memory neural networks via delay‐partitioning approach

“…The state trajectories of the considered delayed discrete-time BAM NNs (1) with its output-feedback control (2) are described in Figure 1. Hence, it is clearly seen through the simulation result in Figure 1 that after a short period of time, the states x 1 (k), x 2 (k), 𝑦 1 (k), and 𝑦 2 (k) converge to zero subject to the prescribed control (2).…”

“…, and Σ 4 = Σ4 = 0, we obtain the dissipative performance of the delayed BAM NNs (1), where 𝛾 1 and 𝛾 2 are also the tuning parameters involved in determining the strict dissipative of discrete-time NNs. iii) When Σ 1 = Σ1 = −I, Σ 2 = Σ2 = 0, Σ 3 = 𝛾 2 1 I, Σ3 = 𝛾 2 2 I, and Σ 4 = Σ4 = 0, the extended dissipative performance is reduced to H ∞ performance of the considered delayed BAM NNs (1). iv) Defining…”

“…In this section, numerical examples are addressed with simulation results to illustrate the sustainability of the proposed delay-partitioning approach for the discrete-time BAM NNs (1) subject to the output-feedback control design (2).…”

“…The bidirectional associative memory (BAM) neural networks (NNs) are widely used artificial NNs that is featured by their ability to store a pair of analog patterns using the real-time unsupervised learning [1,2]. In recent days, the BAM NNs have attracted considerable research attention and have been widely investigated to analyze information memory and association.…”