Resolvent-based approach for $$\pmb {H_2}$$-optimal estimation and control: an application to the cylinder flow

We consider estimation and control of the cylinder wake at low Reynolds numbers. A particular focus is on development efficient numerical algorithms to design optimal linear feedback controllers when there are many inputs (disturbances applied everywhere) outputs (perturbations measured everywhere). propose a resolvent-based iterative algorithm perform i) flow using limited number sensors; ii) entire known but only actuators available for control. The method uses resolvent analysis take advantage low-rank characteristics solutions obtained without any model-order reduction. Optimal also by combining problems. show that performance estimators converges true global optima, indicating important physical mechanisms rank.