Discrete-time Indefinite Stochastic LQ Optimal Control: Infinite Horizon Case

The asymptotic analysis method is applied to the infinite horizon discrete-time indefinite stochastic LQ problem. This paper carries out the research on the basis of the results of its finite horizon counterpart and the mean-square stabilizing assumption. Properties of the solutions to the generalized algebraic Riccati equation (GARE) are also considered. Finally, two examples are provided to justify the developed theory.