Reachable sets bounding for switched systems with time-varying delay and bounded disturbances

ABSTRACT

In this paper, we address the problem of finding outer bound of forward reachable sets and inter-bound of backward reachable sets of switched systems with an interval time-varying delay and bounded disturbances. By constructing a flexible Lyapunov–Krasovskii functional combining with some recent refined integral-based inequalities, some 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. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

KEYWORDS:

• Switched delay systems
• forward reachable sets
• backward reachable sets
• Lyapunov–Krasovskii functional
• linear matrix inequalities

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 ARC (Grant DP130101532) and the Ministry of Education and Training of Vietnam.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the ARC [grant number DP130101532] and the Ministry of Education and Training of Vietnam.