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This work investigates the almost sure stabilization of a class of regime-switching systems based on discrete time observations of both continuous and discrete components. It develops Shao's work SIAM J. Control Optim., 55 (2017), pp. 724--740 in two aspects: first, to provide sufficient conditions for almost sure stability in lieu of moment stability; second, to investigate a class of state-dependent regime-switching processes instead of state-independent ones. To realize these developments, we establish an estimation of the exponential functional of Markov chains based on the spectral theory of linear operator. Moreover, through constructing order-preserving coupling processes based on Skorokhod's representation of jumping process, we realize the control from up and below of the evolution of state-dependent switching process by state-independent Markov chains.
Shao et al. (Tue,) studied this question.