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

The paper is concerned with recursive methods for obtaining the stabilizing solution of coupled algebraic Riccati equations arising in the linear-quad ratic control of Markovian jump linear systems by solving at each iteration uncoupled algebraic Riccati equations. It is shown that the new updates ca rried out at each iteration represent approximations of the original contro l problem by control problems with receding horizon, for which some sequenc es of stopping times define the terminal time. Under this approach, unlike previous results, no initialization conditions are required to guarantee th e convergence of the algorithms. The methods can be ordered in terms of num ber of iterations to reach convergence, and comparisons with existing metho ds in the current literature are also presented. Also, we extend and genera lize current results in the literature for the existence of the mean-square stabilizing solution of coupled algebraic Riccati equations.