The Kullback-Leibler rate metric for comparing dynamical systems

This paper is concerned with information theoretic ¿metrics¿ for comparing two dynamical systems. Following the recent work of Tryphon Georgiou [1], we outline a prediction (filtering) based approach to do so. Central to the considerations of this paper is the notion of uncertainty. In particular, we compare systems in terms of additional uncertainty that results for the prediction problem with an incorrect choice of the model. While [1] used variance of the prediction error, we quantify the extra uncertainty in terms of the Kullback-Leibler divergence rate. This metric is closely related to the classical Bode formula in control theory and we provide detailed comparison to the variance based metric.