Finite-time input-to-state stability and settling-time estimation of impulsive switched systems with multiple impulses

This paper investigates finite-time input-to-state stability (FT-ISS) of impulsive switched systems with multiple impulses. Some FT-ISS conditions, using Lyapunov method and dwell-time condition, are established for impulsive switched systems involving destabilizing and stabilizing impulses simultaneously. When constituent modes regulating continuous dynamics are FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the FTISS is retained if impulsive-switching signal satisfies some dwell-time condition. When some constituent modes regulating continuous dynamics are not FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the impulsive-switching signal which satisfies some dwell-time conditions can achieve the FT-ISS of system. In addition, the settling time can be derived conveniently for certain impulsive-switching signal that is formalized by dwell-time condition. The estimation of settling time presents a class of uniformity with respect to the impulsive-switching signals. Two examples are finally presented for the proposed FT-ISS results.