The finite-time stability problem for state-dependent impulsive dynamical linear systems (SD-IDLS) is addressed in this note. SD-IDLS are a special class of hybrid systems which exhibit jumps when the state trajectory reaches aresettingset. A sufficient condition for finite-time stability of SD-IDLS is provided.S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of Differential Linear Matrix Inequalities. Since such a formulation may be in general more conservative, a procedure which permits to automate its verification, without introduce conservatism, is given both for second order systems, and when the resetting set isellipsoidal.
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Ambrosino et al. (2009) studied this question.
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