a b s t r a c tIn this paper, a necessary and sufficient condition for the exponential stability of linear systems with several time-delays is presented. Such a condition is based on the construction of quadratic lower bounds for the Lyapunov-Krasovskii functionals on the special Razumikhin-type set of functions. The result reveals a constructive procedure for the stability analysis whose application is illustrated with examples.
Abstract-In this paper, for a class of linear time-invariant systems with distributed delay, the robust stability conditions are obtained, and the exponential estimates for the solutions are constructed. The results are derived within the framework of the Lyapunov-Krasovskii functionals with a given derivative. The functional, that does not admit a quadratic lower bound and therefore is considered to be inappropriate for the robustness analysis, is used.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.