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Stability analysis and control of linear impulsive systems is addressed in ahybrid framework, through the use of continuous-time time-varying discontinuousLyapunov functions. Necessary and sufficient conditions for stability ofimpulsive systems with periodic impulses are first provided in order to set upthe main ideas. Extensions to stability of aperiodic systems under minimum,maximum and ranged dwell-times are then derived. By exploiting further theparticular structure of the stability conditions, the results arenon-conservatively extended to quadratic stability analysis of linear uncertainimpulsive systems. These stability criteria are, in turn, losslessly extendedto stabilization using a particular, yet broad enough, class of state-feedbackcontrollers, providing then a convex solution to the open problem of robustdwell-time stabilization of impulsive systems using hybrid stability criteria.Relying finally on the representability of sampled-data systems as impulsivesystems, the problems of robust stability analysis and robust stabilization ofperiodic and aperiodic uncertain sampled-data systems are straightforwardlysolved using the same ideas. Several examples are discussed in order to showthe effectiveness and reduced complexity of the proposed approach.

Convex conditions for robust stability analysis and stabilization of  linear aperiodic impulsive and sampled-data systems under dwell-time  constraints