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Trinh, H.; Nam, Phan T.; Pathirana, Pubudu N.; Le, H. P.

On backwards and forwards reachable sets bounding for perturbed time-delay systems. (English) Zbl 1410.93017

Appl. Math. Comput. 269, 664-673 (2015).
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.

Cited in 10 Documents

MSC:

93B03 Attainable sets, reachability
93C23 Control/observation systems governed by functional-differential equations
93C73 Perturbations in control/observation systems
93C05 Linear systems in control theory

Keywords:

forwards reachable set; backwards reachable set; perturbed time-delay systems; Lyapunov-krasovskii method
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References:

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