An Entropy Formula for Time-Varying Discrete-Time Control Systems

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 $\cW$-transform which generalizes the usual $\cZ$-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying $f$ 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.

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