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Stabilization of regime-switching processes by feedback control based on discrete time observations II: state-dependent case
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.Comment: 33 page