Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays
研究了具有时变时滞和峰值扰动的马尔可夫跳跃神经网络的可达集估计问题，通过Lyapunov-Krasovskii定理和不等式方法，找到了一个尽可能小的椭球集来约束所有状态轨迹，并推广到转移概率不完全的情况。
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.