Delay-dependent conditions for finite time stability of linear time-varying systems with delay

This paper investigates the problem of finite time stability of linear time-varying system with delay. By constructing an augmented time-varying Lyapunov functional and using the Wirtinger-type inequality deductively, delay-dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.