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Filtering deals with the optimal estimation of signals from their noisy observations. The standard setting consists of a pair of random processes (X, Y) = (Xt, Yt) t≥0 , where the signal component X is to be estimated at a current time t > 0 on the basis of the trajectory of Y , observed up to t. Under the minimal mean square error criterion, the optimal… (More)
— Under the structural assumption of stochastic stability, we prove existence of maximal solution for a certain perturbed algebraic Riccati equation in infinite dimensional Banach space. The positive perturbation operator is as it appears in control problems involving Markov jump linear systems with infinite countable state space.
— Uniform convergence of standard transition matrices is a concept which appears in some fundamental results in Markov chain theory and therefore in optimal control, H∞ control and stability problems of continuous-time Markov Jump Linear Systems (MJLSs) with infinite countable state space of the Markov chain. We identify some classes of standard transition… (More)
In this paper we revisit the maximal solution problem studied in . It is shown that, for the Markovian jump scenario, we can get rid of an inconvenient technical hypothesis used in  (originally introduced in ). This is achieved, essentially, via the mean square stability concept.