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Type: Journal article
Title: Reachable set estimation for Markovian jump neural networks with time-varying delays
Author: Xu, Z.
Su, H.
Shi, P.
Lu, R.
Wu, Z.
Citation: IEEE Transactions on Cybernetics, 2017; 47(10):3208-3217
Publisher: IEEE
Issue Date: 2017
ISSN: 2168-2267
Statement of
Zhaowen Xu, Hongye Su, Peng Shi, Renquan Lu, Zheng-Guang Wu
Abstract: 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.
Keywords: Markovian jump systems; neural networks (NNs); reachable set estimation
Rights: © 2016 IEEE.
DOI: 10.1109/TCYB.2016.2623800
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Electrical and Electronic Engineering publications

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