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We provide novel sufficient conditions for stability of nonlinear andtime-varying impulsive systems. These conditions generalize, extend, andstrengthen many existing results. Different types of input-to-state stability(ISS), as well as zero-input global uniform asymptotic stability (0-GUAS), arecovered by employing a two-measure framework and considering stability of bothweak (decay depends only on elapsed time) and strong (decay depends on elapsedtime and the number of impulses) flavors. By contrast to many existing results,the stability state bounds imposed are uniform with respect to initial time andalso with respect to classes of impulse-time sequences where the impulsefrequency is eventually uniformly bounded. We show that the considered classesof impulse-time sequences are substantially broader than other previouslyconsidered classes, such as those having fixed or (reverse) average dwelltimes, or impulse frequency achieving uniform convergence to a limit (superioror inferior). Moreover, our sufficient conditions are not more restrictive thanexisting ones when particularized to some of the cases covered in theliterature, and hence in these cases our results allow to strengthen theexisting conclusions.

Uniform stability of nonlinear time-varying impulsive systems with eventually uniformly bounded impulse frequency