@article{894937913cbd4ef987e09808819458f8,

title = "An Algebraic Formula for Performance Bounds of a Weighted H∞ Optimal Control Problem",

abstract = "This article provides performance bounds for a particular \mathcal {H}-\infty model-matching problem. We consider scalar linear time-invariant plants in a one-degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that nonminimum-phase zeros have on the optimal performance and yields easily computable bounds and approximations.",

keywords = "Discrete-Time systems, control, performance bounds",

author = "Peters, {Andres A.} and Vargas, {Francisco J.} and Jie Chen",

note = "Funding Information: Manuscript received February 23, 2020; accepted March 15, 2020. Date of publication March 19, 2020; date of current version January 28, 2021. This work was supported in part by CONICYT FONDECYT under Projects 3160738 and 1171059, in part by the AC3E, Basal Project FB0008, in part by the Hong Kong RGC under the Project CityU 11260016, and in part by City University of Hong Kong under the Project 7005065. Recommended by Associate Editor M. Guay. (Corresponding author: Andr{\'e}s A. Peters.) Andr{\'e}s A. Peters is with the Departamento de Electricidad, Facultad de Ingenier{\'i}a, Universidad Tecnol{\'o}gica Metropolitana, Santiago, Chile (e-mail: a.petersr@utem.cl). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2021",

month = feb,

doi = "10.1109/TAC.2020.2982135",

language = "English",

volume = "66",

pages = "781--786",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "2",

}