Stability of asynchronous systems with Poisson transitions

We consider the stability of an asynchronous system modeled as a collection of coupled processes with independent Poisson state transitions. Using Lyapunov functions, sufficient conditions for both mean square and almost sure convergence independent of state transition rates are developed for the linear case, and weaker transition rate dependent conditions are derived for the linear and nonlinear case. An illustrative example is discussed and simulated.<
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