A new iteration to coupled discrete-time generalized Riccati equations

Abstract

We consider a set of discrete-time generalized Riccati equations that arise in quadratic optimal control of discrete-time stochastic systems subjected to both state-dependent noise and Markovian jumps. The iterative method to compute the maximal and stabilizing solution of wide class of discrete-time nonlinear equations is derived by Dragan et al. (Int J Control 83(4):837–847, 2010). Here we introduce a new approach to compute the maximal solution of a system of discrete-time generalized Riccati equations. Convergence properties of the new iteration are analyzed. Numerical experiments have been executed and numerical effectiveness estimated.