### 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 language | English (US) |
---|---|

Pages (from-to) | 1691-1706 |

Number of pages | 16 |

Journal | SIAM Journal on Control and Optimization |

Volume | 34 |

Issue number | 5 |

State | Published - Sep 1996 |

### Fingerprint

### Keywords

- Optimal control
- Spectral factorizations
- Time-varying systems

### ASJC Scopus subject areas

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

### Cite this

*SIAM Journal on Control and Optimization*,

*34*(5), 1691-1706.

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

Research output: Contribution to journal › Article

*SIAM Journal on Control and Optimization*, vol. 34, no. 5, pp. 1691-1706.

}

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 -