IEEE Trans Cybern. 2017 Oct;47(10):3208-3217. doi: 10.1109/TCYB.2016.2623800. Epub 2016 Nov 15.
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.
本文研究了具有时变时滞和有界峰值干扰的马尔可夫跳跃神经网络（NNs）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，该集合可以约束零初始条件下 NNs 的所有状态轨迹。在 Lyapunov-Krasovskii 定理的框架内，使用新发现的求和不等式和互凸逼近方法来约束所提出的 Lyapunov 函数的差。建立了一个新的、更保守的条件，该条件与上界、下界和时滞范围有关，以保证状态轨迹被限制在一个类似椭球的集合内。然后，将结果扩展到具有不完全转移概率的情况，并得出了一个更一般的条件。最后，通过一个遗传调控网络的例子来说明本文所得结果的有效性和实用性。
