Solutions for the linear quadratic control problem of Markov jump linear systems

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Abstract
The paper deals with recursive methods for obtaining the stabilizing solution of coupled algebraic Riccati equations arising in the linear quadratic control for Markovian jump linear systems. It is shown that the new updates carried out at each iteration represent approximations of the original control problem by control problems with receding horizon, for which some sequences of stopping times define the terminal time. Unlike previous results, no initialization conditions are required to guarantee the convergence of the algorithms. The methods can be ordered in terms of number of iterations to reach convergence, and comparisons with existing methods in the current literature are also presented. Moreover, we also extend and generalize current results in the literature for the existence of the mean square stabilizing solution of the coupled algebraic Riccati equations.