Stability and control on stochastic time scales.

We develop the stability theory for two classes of dynamic equations evolving on a time domain that is non-uniform and stochastic. In particular, we examine the mean-square exponential stability and almost sure exponential stability of linear, time invariant systems and of linear, time-varying systems, where the variation in time is only due to the local time step. With the stability theory in hand, we apply our results to control systems evolving on stochastic, non-uniform time domains. We design stabilizing closed-loop feedback controllers, observers, observer-based closed-loop feedback controllers, and optimal closed-loop feedback controllers.