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 |
| DOIs | |
| State | Published - Sep 1996 |
Keywords
- Optimal control
- Spectral factorizations
- Time-varying systems
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics