Abstract
In this paper, the problem of delay-dependent stability is investigated for uncertain Markovian jump neural networks with leakage delay, two additive time-varying delay components, and nonlinear perturbations. The Markovian jumping parameters in the connection weight matrices and two additive time-varying delay components are assumed to be different in the system model, and the Markovian jumping parameters in each of the two additive time-varying delay components are also different. The relationship between the time-varying delays and their upper delay bounds is efficiently utilized to study the suggested system in two cases: with known or unknown parameters, which leads to more information of the lower and upper bounds of the time-varying delays that can be used. By constructing a newly augmented Lyapunov-Krasovskii functional and using the extended Wirtinger inequality and a reciprocally convex method, several sufficient criteria are derived to guarantee the stability of the proposed model. Numerical examples and their simulations are given to show the effectiveness and advantage of the proposed method.
Highlights
Over the last decades, considerable attention has been devoted to the study of neural networks because they have been extensively applied in many areas, such as signal processing, optimization problem, static image treatment, and so on [ – ]
A special type of time delay, namely, leakage delay, is a time delay that exists in the negative feedback terms of the system which has a tendency to destabilize a system [ – ]
In this paper, t t–σ x(s) ds and x(t are considered as the elements of augmented vector in V ; in addition, t s x(u) du and t s x (u) du are included in Remark Different from [, ], this article fully considers the relationship between time-varying delays and their upper bounds, different methods are used to enlarge the time-derivative of the Lyapunov-Krasovskii functional appropriately according to different values of the time delay h(t)
Summary
Considerable attention has been devoted to the study of neural networks because they have been extensively applied in many areas, such as signal processing, optimization problem, static image treatment, and so on [ – ]. The Markovian jump neural network is investigated in [ ], in the considered system, two additive time-delay components are two mode-dependent time-varying delays, which have the same Markovian jumping parameters with connection weight matrices. According to the relationship ≤ d (t) ≤ d and d (t) ≤ d(t) ≤ d, the authors consider two cases while calculating the derivative of the Lyapunov functional: d(t) ∈ [d (t), d ) and d(t) ∈ [d , d] This method has not been fully used to investigate the robust stability of Markovian jump neural networks with two additive time-varying delay components. Since the relationship between time-varying delays and their upper bounds is fully considered, the extended reciprocally convex approach in [ ] will be used to deal with the robust stability problem of Markovian jump neural networks with two additive time-varying delay components.
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