Lyapunov conditions for input-to-state stability of impulsive systems

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Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods (2010, methodology): “Note that in [12] this theorem was proved, using exponential ISS Lyapunov functions in dissipative form.”
Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects (2017, methodology): “Definition 2 ([9]) For an impulsive sequence 1tk; k 2 No, let N.”
Characterizations of input-to-state stability for hybrid systems (2009, background): “Some work related to ISS in switched systems with arbitrary switching signals has appeared in [14], and Lyapunov conditions for ISS in impulsive systems have been reported in [8].”
Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects (2018, neutral): “i=1 m̄i(k0))e −k0) + nd̄ (1 − e−α)d ||w||[k0,k−1], (14)”
Input-to-state stability of impulsive and switching hybrid systems with time-delay (2011, background): “The above definitions are parallel to the ones given in Chen and Zheng (2009), Hespanha et al. (2008) and Pepe and Jiang (2006).”