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

This letter 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 param...

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Bibliographic Details
Published inIEEE control systems letters Vol. 3; no. 4; pp. 1014 - 1019
Main Authors Furieri, Luca, Yang Zheng, Papachristodoulou, Antonis, Kamgarpour, Maryam
Format Journal Article
LanguageEnglish
Published IEEE 01.10.2019
Subjects
Adaptive control
distributed control
Indexes
Linear systems
Optimal control
Programming
Subspace constraints
Transfer functions
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Summary:This letter 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.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2019.2920205