Finite-Time Stability of Time-Delay Switched Systems with Delayed Impulse Effects

This paper investigates the finite-time stability problem for a class of time-delay switched systems with nonlinear perturbation and delayed impulse effects. Based on the Lyapunov function method and the technique of inequalities, stability criteria are established to guarantee that the state trajectory of the system does not exceed a certain threshold over a pre-specified finite time interval. Compared with existing results for related problems, the obtained results can be applied to a larger class of hybrid delayed systems, including those in which all of the subsystems are stable and unstable. Two examples are given to demonstrate the validity of the main results.