Performance bounds in ℋ∞ optimal control for stable SISO plants with arbitrary relative degree

Andrés A. Peters; Mario E. Salgado

doi:10.1109/TAC.2009.2023966

Performance bounds in ℋ_∞ optimal control for stable SISO plants with arbitrary relative degree

Andrés A. Peters, Mario E. Salgado

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

This note deals with performance bounds for the ℋ_∞ -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal ℋ_∞ cost as a function of the plant relative degree.

Original language	English
Pages (from-to)	1987-1990
Number of pages	4
Journal	IEEE Transactions on Automatic Control
Volume	54
Issue number	8
DOIs	https://doi.org/10.1109/TAC.2009.2023966
State	Published - 2009

Keywords

Discrete-time systems
H-infinity control
Performance bounds

Access to Document

10.1109/TAC.2009.2023966

Cite this

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title = "Performance bounds in ℋ∞ optimal control for stable SISO plants with arbitrary relative degree",

abstract = "This note deals with performance bounds for the ℋ∞ -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal ℋ∞ cost as a function of the plant relative degree.",

keywords = "Discrete-time systems, H-infinity control, Performance bounds",

author = "Peters, {Andr{\'e}s A.} and Salgado, {Mario E.}",

note = "Funding Information: Manuscript received November 28, 2008; revised March 04, 2009. Current version published August 05, 2009. This work was supported by UTFSM and Fondecyt-Chile through Grant 1080274. Recommended by Associate Editor D. Arzelier.",

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AU - Salgado, Mario E.

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N2 - This note deals with performance bounds for the ℋ∞ -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal ℋ∞ cost as a function of the plant relative degree.

AB - This note deals with performance bounds for the ℋ∞ -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal ℋ∞ cost as a function of the plant relative degree.

KW - Discrete-time systems

KW - H-infinity control

KW - Performance bounds

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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