Epsilon-Entropy and H∞ Entropy in Continuous Time Systems

Abstract

Based on the analysis of ε – entropy, information in continuous time linear multivariable stochastic systems is discussed. To describe time average information variation after a process transmitted through a continuous time system, the concept of system variety defined by the difference between ε – entropy rates of system input and output is proposed. Furthermore, an equivalent relation between system variety and the H∞ entropy, an auxiliary performance index in H∞ control theory, is derived by using spectral factorization. This connection gives information theoretic interpretation to H∞ entropy, and provides new potential method to analyze and design continuous time stochastic systems.