In this paper we study the state-feedback stabilization of a discrete-timeMarkov jump linear system when the observation of the Markov chain of thesystem, called the Markov state, is time-randomized by another Markov chain.Embedding the Markov state into an extended Markov chain, we transform thegiven system with time-randomized observations to another one having theenlarged Markov-state space but with so-called cluster observations of Markovstates. Based on this transformation we propose linear matrix inequalities fordesigning stabilizing state-feedback gains for the original Markov jump linearsystems. The proposed method can treat both periodic observations and many ofrenewal-type observations in a unified manner, which are studied in theliterature using different approaches. A numerical example is provided todemonstrate the obtained result.
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