On stable LQG controllers and cost functional values

Three numerical techniques for achieving stable stabilising LQG controllers have been discussed. The one-step method and the iterative loop on convergence of P method guarantee the stability of the controller. The first method is more direct and yields a more accurate controller since the modified control Riccati equation takes the same form as a general Riccati matrix. The iterative loop on convergence of p method seems to be of technical interest via its connection with the fine tuning method. Finally, the fine tuning method attempts to minimise the suboptimality of the stable stabilising LQG controller. It was most interesting for a robustness recovery property observed. Mention was made of the dual results using a fixed optimal control gain matrix and modifying the filter design. Although full results are available for this approach, it is felt that it is of technical interest only.