# Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances

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## Abstract

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov–Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

## Keywords

Generalized neural networks Forwards reachable sets Backwards reachable sets Lyapunov–Krasovskii functional Linear matrix inequalities## Notes

### Acknowledgments

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 Australian Research Council (Grant DP130101532) and the Ministry of Education and Training of Vietnam.

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