Algorithm Design and Extremum Control: Convex Synthesis due to Plant Multiplier Commutation

A novel convex state-space solution to the robust output-feedback synthesis problem based on dynamic integral quadratic constraints for a particular class of systems is presented. Convexification rests upon the assumption that the control-to-uncertainty block in the generalized plant commutes with the off-diagonal block of the multiplier. We demonstrate that this commutation property is valid for several by themselves interesting concrete scenarios, such as in extremum control, a generalization of the convex design of first-order optimization algorithms involving filtered gradient evaluations.