Almost sure stabilization for linear switching stochastic systems against time-delay in detection of switching signal

We are concerned with stabilization problem for a class of stochastic switching systems with time-delay in detection of switching signal. By using binomial model, Poisson process, and Wiener process to characterize time-delay, switching signal, and exogenous disturbance, respectively, the problem is set in a stochastic framework. The influence of the random time-delay is combined into reconstructing the switching signal of overall closed-loop system and changes the distribution property of switching points. Therefore, based on the asymptotical behaviors of Poisson processes and Wiener processes, we establish some almost surely exponential stability conditions. Moreover, we pose a design methodology for solving the stabilization control.