On the Equivalence of Youla, System-level and Input-output Parameterizations

Journal article

A 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 characterizations require no doubly-coprime factorization but a set of equality constraints for achievable closed-loop responses. In this paper, we present explicit affine mappings among Youla, system-level and input-output parameterizations. Two direct implications of the affine mappings are 1) any convex problem in 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 (SLS); 2) the condition of quadratic invariance (QI) is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of Youla, system-level, or input-output parameters.

Authors: Zheng, Y; Furieri, L; Papachristodoulou, A; Li, N; Kamgarpour, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Electrical and Electronics Engineers
• Journal: IEEE Transactions on Automatic Control More from this journal
• Volume: 66
• Issue: 1
• Pages: 413 - 420
• Publication date: 2020-03-10
• Acceptance date: 2020-02-29
• DOI: 10.1109/tac.2020.2979785
• EISSN: 2334-3303
• ISSN: 0018-9286
• Language: English
• Keywords: Electronic mail; Decentralized control; FFR; Linear systems; Stabilizing controller; Quadratic invariance; System-level synthesis; Task analysis; Optimal control; Youla parameterization; Closed loop systems; Adaptive control