Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control.

This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.