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New Results on Reachable Sets Bounding for Switched Neural Networks Systems with Discrete, Distributed Delays and Bounded Disturbances

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Abstract

In this paper, problem of reachable sets bounding is considered for switched neural networks systems with mixed time-varying delays and bounded disturbances. By using Lyapunov–Krasovskii functional method, some new sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

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Acknowledgements

The author would like to thank the editor(s) and anonymous reviewers for their constructive comments which helped to improve the present paper. This work was partially supported by the Ministry of Education and Training of Vietnam.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Thainguyen University of Science, Thainguyen, Vietnam

    Mai Viet Thuan

  2. Faculty of General Science, Hanoi University of Natural Resources and Environment, Hanoi, Vietnam

    Nguyen Thi Huyen Thu

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  1. Mai Viet Thuan
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  2. Nguyen Thi Huyen Thu
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Correspondence to Mai Viet Thuan.

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Thuan, M.V., Thu, N.T.H. New Results on Reachable Sets Bounding for Switched Neural Networks Systems with Discrete, Distributed Delays and Bounded Disturbances. Neural Process Lett 46, 355–378 (2017). https://doi.org/10.1007/s11063-017-9596-4

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