Appendix: Covariance Functions and Dissipative Systems

Jan H. van Schuppen*

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific

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.

Original languageEnglish
Title of host publicationControl and System Theory of Discrete-Time Stochastic Systems
PublisherSpringer
Pages883-896
Number of pages14
ISBN (Electronic)978-3-030-66952-2
DOIs
Publication statusPublished - 2021

Publication series

NameCommunications and Control Engineering
ISSN (Print)0178-5354
ISSN (Electronic)2197-7119

Keywords

  • Covariance function
  • Dissipative system
  • Storage function

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