On the observability of continuous time linear systems with Markov jump parameters

This paper studies observability of a class of Markov systems with jumping parameters, and an associated set of observability matrices. We explore some invariance results in order to demonstrate a certain property involving those matrices. This property is known in the literature of this class of systems, but there is no available proof. The obtained results are technically involving and important, as they validate many existing results that rely on that property.