On strong convergence of feedback operators for non-normal distributed parameter systems

We consider the question of strong convergence of the functional gains for LQR/LQG control laws of delay systems. The feedback operators for such systems can be defined in terms of solutions of operator Riccati equations. It has been known for some time that dual convergence is sufficient for strong convergence of the corresponding feedback operators. In this paper, we conjecture that dual convergence is also necessary. Numerical examples are presented to illustrate this point. Finally, we close with a specific conjecture and discuss some previous results along this line.