An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis

• Published in: arXiv.org
• Main Authors: Furieri, Luca, Yang, Zheng, Papachristodoulou, Antonis, Kamgarpour, Maryam
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.07.2020
• Subjects: Computational geometry; Computer Science - Systems and Control; Controllers; Convexity; Design parameters; Feedback control; Invariants; Mathematical programming; Mathematics - Optimization and Control; Output feedback; Parameterization; Programmable logic devices; Transfer matrices
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1903.03828

This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.