LMI-based criteria for robust finite-time stabilisation of switched systems with interval time-varying delay

This study investigates the problem of finite-time stabilisation for a class of switched linear systems with interval time-varying delay and parametric uncertainties. First, sufficient conditions for the finite-time stability of unforced switched systems are presented based on the average dwell time method and on the appropriate multiple Lyapunov-like functions that contain information regarding the lower and upper bounds of delay. A state feedback controller is then proposed for uncertain switched systems, with interval time-varying delay, which guarantees finite-time stabilisation of closed-loop systems. These conditions are formulated using a set of linear matrix inequalities and are dependent on the size of the time delay. Moreover, the criteria obtained are less conservative than some existing results because of the assumption of the upper bound of the derivative of the Lyapunov-like functions, without the neglect of any useful terms. Finally, two examples are provided to demonstrate the effectiveness of the proposed method. The first is a numerical example, and the second is a practical example involving river pollution control.