On backwards and forwards reachable sets bounding for perturbed time-delay systems

Trinh, Hieu, Nam, Phan T., Pathirana, Pubudu N. and Le, H.P. 2015, On backwards and forwards reachable sets bounding for perturbed time-delay systems, Applied mathematics and computation, vol. 269, pp. 664-673, doi: 10.1016/j.amc.2015.07.116.

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Title On backwards and forwards reachable sets bounding for perturbed time-delay systems
Author(s) Trinh, HieuORCID iD for Trinh, Hieu orcid.org/0000-0003-3438-9969
Nam, Phan T.
Pathirana, Pubudu N.ORCID iD for Pathirana, Pubudu N. orcid.org/0000-0001-8014-7798
Le, H.P.
Journal name Applied mathematics and computation
Volume number 269
Start page 664
End page 673
Total pages 10
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2015-08-24
ISSN 0096-3003
1873-5649
Keyword(s) Backwards reachable set
Forwards reachable set
Lyapunov-Krasovskii method
Perturbed time-delay systems
Summary Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov-Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.
Language eng
DOI 10.1016/j.amc.2015.07.116
Field of Research 010203 Calculus of Variations, Systems Theory and Control Theory
010204 Dynamical Systems in Applications
090602 Control Systems, Robotics and Automation
Socio Economic Objective 970109 Expanding Knowledge in Engineering
HERDC Research category C1 Refereed article in a scholarly journal
Grant ID DP130101532
Copyright notice ©2015, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30077864

Document type: Journal Article
Collection: School of Engineering
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