An Improved Method for Solving a System of Discrete-Time Generalized Riccati Equations
Ivan Ganchev Ivanov · 2011
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 for a wide class of discrete-time nonlinear equations was derived by Dragan, Morozan and Stoica (International Journal of Control 83, (2010), 837-847). Here we modify this method and illustrate it in the computation of the maximal solution of a system of discrete-time generalized Riccati equations. Convergence properties of this method are analyzed. Numerical experiments are reported to estimate the effectiveness of this new iterative method.