Stability of linear systems with time-varying delays: an Lyapunov functional approach

A new stability criterion for linear systems with multiple time-varying delays is established by employing the method of Lyapunov functional based on the Lyapunov-Krasovskii theorem. This criterion has only one positive definite tuning parameter matrix in two LMIs, one LMI is exactly the same as the stability criteria for the corresponding system without delay and the other restrict on influence of delay. It is analytically shown the presented result is less conservative than those proposed theorems and techniques in the literature recently. Examples are given to show the application of the established stability theorem.