Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications.

This paper investigates the finite time stability (FTS) for nonlinear impulsive sampled-data systems. By constructing an appropriated Lyapunov function and employing average impulsive interval (AII) method, some FTS criteria for the nonlinear impulsive sampled-data systems are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. The hybrid controller including sampled-data controller and impulsive controller is designed via the established LMIs. Moreover, the impulse effect considered in this paper including stabilizing impulse and destabilizing impulse. Our developed results are less conservative than the recent work in the literature. Finally, two numerical examples are provided to show the applications of the proposed criteria.