Decoupled Stein iterations to the discrete-time generalized Riccati equations

The authors investigate the numerical solution of a set of discrete-time generalised Riccati equations. The class of discrete-time non-linear equations involves in various control problems for discrete-time stochastic systems and it can be considered as an important tool for solving optimisation control for such type systems. A new procedure for computing the maximal solution and the stabilising solution is proposed by Dragan et al. (`Iterative algorithm to compute the maximal and stabilising solutions of a general class of discrete-time Riccati-type equations`, Int. J. Control, 2010, 83, (4), pp. 837-847). In this study, the authors introduce a new iterative procedure based on the solution of a Stein matrix equation for computing the maximal and the stabilising solution. The convergence properties of the new iteration are proved. Sufficient conditions for computing the maximal solution and the stabilising solution are derived. Finally, some numerical examples are presented to illustrate the feasibility of the proposed algorithm.