Abstract
In this paper, a suitable Lyapunov-Krasovskii functional together with the inequality analysis technique for neutral-type system, and sufficient exponential stability conditions are proposed in the form of linear matrix inequalities (LMIs). Firstly, the system model of leakage delay and semi-Markovian process for neutral-type neural network is established, where the sojourn-time follows Weibull distribution, which is time-varying instead of being constant in the transition rate. Secondly, through combinations of stability analysis method, Lyapunov-Krasovskii functional and inequality analysis technique, some sufficient conditions have been achieved to undertake the exponential stabilization of given neural network system. Moreover, time delays of the system contain leakage and mixed delays, which are more general and appropriate. Finally, in order to show the many advantages of our model, the obtained results will be compared with previous works based on methods different from semi-Markovian jump or leakage delay.
Highlights
In the past decades, neural networks have been found in extensive studies [1]–[3] where time delay is a fundamental concept
This paper aims to investigate exponential stability of neutral-type neural network with leakage delay and semi-Markovian jump
Based on exponential stability theory, new exponential stability condition for neutral-type neural network with mixed, leakage delays and semi-Markovian jump will be investigated in terms of linear matrix inequalities (LMIs)
Summary
Neural networks have been found in extensive studies [1]–[3] where time delay is a fundamental concept. In [19], Shu discussed Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and α-inverse Hölder activation functions. This paper aims to investigate exponential stability of neutral-type neural network with leakage delay and semi-Markovian jump. Based on exponential stability theory, new exponential stability condition for neutral-type neural network with mixed, leakage delays and semi-Markovian jump will be investigated in terms of LMIs. The contributions of this paper can be summarized as follows: VOLUME 8, 2020. Based on the discussions in the section above, we consider the following semi-Markovian jumping neutral-type neural network systems with mixed and leakage delays: d[x(t) − E(r(t))x(t − h(t))]. To the best of our knowledge, there have not been any exponential stability conditions for neutral-type neural networks with leakage delay and semi-Markovian jump has been addressed first time in this paper. Theorem 1 considers the different time delays and semi-Markovian jump
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