Global stabilization of linear discrete-time systems with bounded feedback

Yudi Yang; Eduardo D. Sontag; Hector J. Sussmann

doi:10.1016/S0167-6911(97)00021-2

Global stabilization of linear discrete-time systems with bounded feedback

Yudi Yang, Eduardo D. Sontag, Hector J. Sussmann

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

69 Scopus citations

Abstract

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions.

Original language	English (US)
Pages (from-to)	273-281
Number of pages	9
Journal	Systems and Control Letters
Volume	30
Issue number	5
DOIs	https://doi.org/10.1016/S0167-6911(97)00021-2
State	Published - Jun 1997

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science(all)
Mechanical Engineering
Electrical and Electronic Engineering

Keywords

Global stabilization
Linear discrete-time systems
Saturated feedback

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10.1016/S0167-6911(97)00021-2

Cite this

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title = "Global stabilization of linear discrete-time systems with bounded feedback",

abstract = "This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ({"}single hidden layer neural networks{"}) of simple saturation functions.",

keywords = "Global stabilization, Linear discrete-time systems, Saturated feedback",

author = "Yudi Yang and Sontag, {Eduardo D.} and Sussmann, {Hector J.}",

note = "Funding Information: * Corresponding author. E-mail: yudiy@vnet.ibm.com. I Supported in part by US Air Force Grant AFOSR-94-0343. 2 Supported in part by NSF Grant DMS-8902994 and by US Air Force Grant AFOSR-94-0343.",

year = "1997",

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doi = "10.1016/S0167-6911(97)00021-2",

language = "English (US)",

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T1 - Global stabilization of linear discrete-time systems with bounded feedback

AU - Yang, Yudi

AU - Sontag, Eduardo D.

AU - Sussmann, Hector J.

N1 - Funding Information: * Corresponding author. E-mail: yudiy@vnet.ibm.com. I Supported in part by US Air Force Grant AFOSR-94-0343. 2 Supported in part by NSF Grant DMS-8902994 and by US Air Force Grant AFOSR-94-0343.

PY - 1997/6

Y1 - 1997/6

N2 - This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions.

AB - This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions.

KW - Global stabilization

KW - Linear discrete-time systems

KW - Saturated feedback

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DO - 10.1016/S0167-6911(97)00021-2

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VL - 30

SP - 273

EP - 281

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 5

ER -

Global stabilization of linear discrete-time systems with bounded feedback

Abstract

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