On detectability and observability of discrete-time stochastic Markov jump systems with state-dependent noise

This paper mainly studies the notions of detectability and observability for discrete-time stochastic Markov jump systems with state-dependent noise. Two concepts called “W-detectability” and “W-observability” for such systems are introduced, which are shown to coincide with exact detectability and exact observability reported recently in literatures. Moreover, some criteria and interesting properties for both W-detectability and W-observability are obtained.