Exponential stability almost surely of linear dynamical systems on stochastic pulse time scales

In this paper, we expand the stability theory of dynamical systems on stochastic time scales to the case of stochastic pulse time scales. The class of systems considered here evolve on nonuniform time-domains that consist of a union of disjoint closed intervals with stochastic lengths, followed by random step sizes. Necessary and sufficient conditions for exponential stability almost surely are derived. The approach is based on determining the region of exponential stability almost surely. An illustrative numerical example is presented to validate the results. The class of systems considered in this paper has important applications for example, control networks subject to communications failures, population dynamics, signal processing with variable sampling, consensus multi-agents systems and wide-area power system controls.