Parameterization approach to stability and feedback stabilization of linear time-delay systems

This paper develops a new parameterized approach to the problems of delay-dependent analysis and feedback stabilization for a class of linear continuous-time systems with time-varying delays. An appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics. The construction guarantees avoiding bounding methods and effectively deploying injecting parametrized variables to facilitate systematic analysis. Delay-dependent stability provides a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear time-delay system is asymptotically stable with a c-level L2 gain. By delay-dependent stabilization, a state-feedback scheme is designed to guarantee that the closed-loop switched system enjoys the delay-dependent asymptotic stability with a prescribed c-level L2 gain. It is established that the methodology provides the least conservatism in comparison with other published methods. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.