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This paper is concerned with persistent identification of systems that involve deterministic un-modeled dynamics and stochastic observation disturbances, and whose unknown parameters switch values (possibly large jumps) that can be represented by a Markov chain. Two classes of problems are considered. In the first class, the switching parameters are stochastic processes modeled by irreducible and a periodic Markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms. In this case, tracking real-time parameters by output observations becomes impossible and the authors show that an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with periodic inputs and least-squares type algorithms.
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