Renyi Entropy of Multivariate Autoregressive Moving Average Control Systems

The Renyi entropy is an important measure of the information, it is proposed by Renyi in the context of entropy theory as a generalization of Shannon entropy. We study in detail this measure of multivariate autoregressive moving average (ARMA) control systems. The characteristic function of output process is represented from the terms of its residual characteristic functions. Simple expression to compute the Renyi entropy for the output process of these systems is derived. In addition, we investigate the covariance matrix for finding the upper bound of the entropy. Finally, we present three separate examples that serve to illustrate the behavior of information in a multivariate ARMA control system where the control and noise distributed as Gaussian, Cauchy and Laplace processes.