This note considers the problem of finite-time stability (FTS) for impulsive switched linear time-varying (LTV) systems. First, two improved necessary and sufficient conditions are proposed to verify the FTS of LTV by employing an indefinite Lyapunov function. Then, the results obtained are extended to study the FTS of impulsive switched LTV systems, two new necessary and sufficient conditions are given by using common indefinite Lyapunov function and piecewise indefinite Lyapunov functions.

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... pared with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems to be indefinite and have a tighter upper bound, moreover, all subsystems are also allowed to be not FTS. Furthermore, the construction method of switching signal is given, moreover, using function-dependent dwell time methods, three sufficient conditions of FTS are also proposed for the systems. Two numerical examples are given to illustrate the theoretical results.