State-feedback stabilization of linear systems with input and state delays

This paper develops new feedback stabilization criteria for a class of linear continuous-time systems with state and input delays. The state-delay is an unknown differentiable time-varying function satisfying some known bounding and the input delay is a known constant to guarantee practical implementation. With focus on state-feedback, an appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics and to avoid bounding methods. Injecting parametrized variables are effectively deployed to facilitate delay-dependent stability analysis and to provide a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear nominal and polytopic feedback systems are asymptotically stable with an γ-level.