Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

Dear Editor, This letter studies finite-time input-to-state stability (FTISS) for impulsive switched systems. A set of Lyapunov-based conditions are established for guaranteeing FTISS property. When constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing, the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time (ADT) condition. When some or even all constituent modes governing continuous dynamics are not FTISS and discrete dynamics involving impulses are stabilizing, the FTISS can be achieved if impulsive-switching signals satisfy a reverse ADT condition. Examples are presented to illustrate the efficiency of proposed results.