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Split optimal policy iteration for LQR problems

This technical report is concerned with the convergence properties of what we call the split optimal policy iteration for coupled LQR problems; see section 3.1 in the manuscript. Interestingly, the iteration shows different convergence behavior for continuous and discrete time systems: while global convergence holds for both cases, we have local quadratic convergence for the continuous time case, but only linear convergence for the discrete time case - even though quadratic convergence is retained in the limit as the coupling between the subsystems vanishes.