New robust stability criteria of systems with time-varying delays

In this paper, we deals with the problem of the robust stability of a linear system with a time-varying delay and polytopic-type uncertainties via homogeneous polynomial forms. An type of transformation related to the homogeneous polynomial function for stability analysis of linear system subject to time-varying parametric uncertainty, affecting rationally the state space matrix, is introduced. In order to obtain less conservative conditions for the system, we investigated a new method of HPLFs to deal with a time-delay system without uncertainties. In this method, the robustness properties can be investigated by using HPLFs, which is a non-conservatives class of Lyapunov functions. Then we can extended this method to the system with polytopic-type uncertainties is easily. Numerical results illustrate the efficiency of the proposed condition, which provide less conservative estimates of stability domains than similar tests in the literature.