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Impulsive systems are a very flexible class of systems that can be used torepresent switched and sampled-data systems. We propose to extend here thepreviously obtained results on deterministic impulsive systems to thestochastic setting. The concepts of mean-square stability and dwell-times areutilized in order to formulate relevant stability conditions for such systems.These conditions are formulated as convex clock-dependent linear matrixinequality conditions that are applicable to robust analysis and controldesign, and are verifiable using discretization or sum of squares techniques.Stability conditions under various dwell-time conditions are obtained andnon-conservatively turned into state-feedback stabilization conditions. Theresults are finally applied to the analysis and control of stochasticsampled-data systems. Several comparative examples demonstrate the accuracy andthe tractability of the approach.

Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints