Zheng, Y.Furieri, L.Papachristodoulou, A.Li, N.Kamgarpour, Maryam2021-12-012021-12-012021-12-01202110.1109/TAC.2020.2979785https://infoscience.epfl.ch/handle/20.500.14299/183299A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doubly coprime factorization of the system, while the recent system-level and input-output parametrizations require no doubly coprime factorization, but a set of equality constraints for achievable closed-loop responses. In this article, we present explicit affine mappings among Youla, system-level, and input-output parameterizations. Two direct implications of these affine mappings are: 1) any convex problem in the Youla, system-level, or input-output parameters can be equivalently and convexly formulated in any other one of these frameworks, including the convex system-level synthesis; 2) the condition of quadratic invariance is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of either Youla, system-level, or input-output parameters. © 1963-2012 IEEE.Quadratic invariance (QI)stabilizing controllersystem-level synthesis (SLS)Youla parameterizationtext::journal::journal article::research article