Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays
Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays
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DOI：
10.1109/tcyb.2016.2623800
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发表时间：
2017-10
影响因子：
11.8
通讯作者：
Zhaowen Xu;H. Su;Peng Shi;Renquan Lu;Zhengguang Wu
中科院分区：
文献类型：
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作者：
Zhaowen Xu;H. Su;Peng Shi;Renquan Lu;Zhengguang Wu
研究了具有时变时滞和有界峰值扰动的马尔可夫跳变神经网络的可达集估计问题。我们的目标是找到一个尽可能小的集合，它在零初始条件下约束所有NN的状态轨迹。在Lyapunov-Krasovskii定理的框架下，一个新发现的求和不等式结合凸的方法被用来限制所提出的李雅普诺夫泛函的差异。建立了一个新的不太保守的条件，依赖于上界，下界和时间延迟的延迟范围，以确保状态轨迹有界的椭球状集。然后将结果推广到不完全转移概率的情形，得到了更一般的条件。最后，包括一个基因调控网络的例子来证明本文所得到的结果的有用性和有效性。
In this paper, the reachable set estimation problem is investigated for Markovian jump neural networks (NNs) with time-varying delays and bounded peak disturbances. Our goal is to find a set as small as possible which bounds all the state trajectories of the NNs under zero initial conditions. In the framework of Lyapunov–Krasovskii theorem, a newly-found summation inequality combined with the reciprocally convex approach is used to bound the difference of the proposed Lyapunov functional. A new less conservative condition dependent on the upper bound, the lower bound and the delay range of the time delay is established to guarantee that the state trajectories are bounded within an ellipsoid-like set. Then the result is extended to the case with incomplete transition probabilities and a more general condition is derived. Finally, examples including a genetic regulatory network are given to demonstrate the usefulness and the effectiveness of the results obtained in this paper.