@inbook{f7de0782adbd4ead8641c339ed9d73ed,
title = "Appendix: Covariance Functions and Dissipative Systems",
abstract = "The concept of a dissipative system is defined for a deterministic linear system and is satisfied if there exists a storage function and a supply rate such that the dissipation inequality holds. It is proven that a deterministic linear system is dissipative if and only if a related function is a positive-definite function. Any covariance function of a stochastic process is a positive-definite function. An equivalence condition is proven for a deterministic linear system to be dissipative in terms of an algebraic condition, a matrix has to satisfy a linear matrix inequality.",
keywords = "Covariance function, Dissipative system, Storage function",
author = "{van Schuppen}, {Jan H.}",
year = "2021",
doi = "10.1007/978-3-030-66952-2_23",
language = "English",
series = "Communications and Control Engineering",
publisher = "Springer",
pages = "883--896",
booktitle = "Control and System Theory of Discrete-Time Stochastic Systems",
}