# Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters

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## Abstract

This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples.

## Keywords

Markov jump Reachable set estimation Bidirectional associative memory NNSs Piecewise-constant transition rates Time delay## Mathematics Subject Classification

00-01 99-00## Notes

### Acknowledgements

This work was supported in part supported by both the National Natural Science Foundation of China under Grants 11401062 and 61374104, NSFC 61374086, the Natural Science Foundation of Jiangsu Province under Grant BK20140770, BK20131097. The authors would like to express sincere appreciation to the editor and anonymous reviewers for their valuable comments which have led to an improvement in the presentation of the paper.

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