An entropy formula for time-varying discrete-time control systems

Research output: Contribution to journalArticle

Abstract

The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of the W-transform which generalizes the usual Z-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying H control, there exists a unique, bounded contraction which maximizes the entropy. This generalizes known results in the time-invariant case. Possible extensions are discussed, along with state-space formulae.

Original languageEnglish (US)
Pages (from-to)1691-1706
Number of pages16
JournalSIAM Journal on Control and Optimization
Volume34
Issue number5
StatePublished - Sep 1996

Fingerprint

Discrete time control systems
Time varying systems
Discrete-time Systems
Time-varying
Entropy
Time-varying Systems
Control System
Z transforms
Generalise
Factorization
Transform
Spectral Factorization
Linear Fractional Transformation
Transfer functions
Mathematical transformations
Transfer Function
Contraction
State Space
Maximise
Invariant

Keywords

  • Optimal control
  • Spectral factorizations
  • Time-varying systems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

Cite this

An entropy formula for time-varying discrete-time control systems. / Iglesias, Pablo A.

In: SIAM Journal on Control and Optimization, Vol. 34, No. 5, 09.1996, p. 1691-1706.

Research output: Contribution to journalArticle

@article{8e656112558e479b8063d05e557d546f,
title = "An entropy formula for time-varying discrete-time control systems",
abstract = "The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of the W-transform which generalizes the usual Z-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying H∞ control, there exists a unique, bounded contraction which maximizes the entropy. This generalizes known results in the time-invariant case. Possible extensions are discussed, along with state-space formulae.",
keywords = "Optimal control, Spectral factorizations, Time-varying systems",
author = "Iglesias, {Pablo A}",
year = "1996",
month = "9",
language = "English (US)",
volume = "34",
pages = "1691--1706",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",

}

TY - JOUR

T1 - An entropy formula for time-varying discrete-time control systems

AU - Iglesias, Pablo A

PY - 1996/9

Y1 - 1996/9

N2 - The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of the W-transform which generalizes the usual Z-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying H∞ control, there exists a unique, bounded contraction which maximizes the entropy. This generalizes known results in the time-invariant case. Possible extensions are discussed, along with state-space formulae.

AB - The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of the W-transform which generalizes the usual Z-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying H∞ control, there exists a unique, bounded contraction which maximizes the entropy. This generalizes known results in the time-invariant case. Possible extensions are discussed, along with state-space formulae.

KW - Optimal control

KW - Spectral factorizations

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=0030242287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030242287&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030242287

VL - 34

SP - 1691

EP - 1706

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 5

ER -