Generalized Linear Time-delay System Finite Time Stabilization And Stabilization Problem Research

In this paper finite-time stability and finite-time stabilization problems for aclass of singular linear time-delay systems with time-varying exogenous disturbancesare studied.First of all, two diferent definitions of finite-time stability for singular lineartime-delay systems are given when the exogenous disturbances are norm bounded.According to these two definitions, two sufcient conditions of the finite-time sta-bility for this kind of systems are presented by combining Lyapunov approach andlinear matrix inequality technique.Then, based on the definitions and sufcient conditions of the finite-time sta-bility for this kind of systems, one finite-time stabilization condition for this kind ofsystems is presented and the corresponding state feedback controller is designed.However, the nonlinear problems which prevent us to get the state feedback gainin the linear matrix inequalities are solved by maximum-eigenvalue and minimum-eigenvalue approach as well as an algorithm so-called cone complementarity lin-earization. Thereby, the considered finite-time stabilization problem via state feed-back controller is solved. The efectiveness of the approaches proposed in this paperare presented by numerical examples.