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

摘要: 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 forwards reachable sets inter backwards system. Firstly, two definitions on sets, where initial state vectors not necessary to be equal zero, introduced. Then, by using Lyapunov-Krasovskii method, sufficient conditions for existence of: (i) smallest possible sets; (ii) largest derived. These presented terms linear matrix inequalities parameters need tuned, which therefore can efficiently solved combining existing convex optimization algorithms a two-dimensional search method obtain optimal bounds. Lastly, obtained results illustrated four numerical examples.