On finite-time stability of state dependent impulsive dynamical systems

This paper extends the finite-time stability problem to state dependent impulsive dynamical systems. For this class of hybrid systems, the state jumps when the trajectory reaches a resetting set, which is a subset of the state space. A sufficient condition for finite-time stability of state dependent impulsive dynamical systems is provided. Moreover, S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of differential linear matrix inequalities (DLMIs). Such a formulation may be in general more conservative, for this reason a procedure which allows to automate its verification, without introduce conservatism, is given both for second order systems, and when the resetting set is ellispoidal.