Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems

Sufficient conditions for the finite-time stability (FTS) of impulsive dynamical linear systems (IDLSs) have been provided in  Amato, Ambrosino, Cosentino, and De Tommasi (2011). In this brief note we show that, when time-dependent IDLSs are dealt with, the sufficient condition for FTS derived in  Amato, Ambrosino, Cosentino et al. (2011) is also necessary. Moreover, an alternative necessary and sufficient condition for FTS is proposed, which is based on the solution of a coupled differential–difference Lyapunov equation. This condition turns out to be more efficient from the computational point of view. The proposed approach is illustrated through some examples.