Appendix

van Schuppen, J.H.

Appendix

Covariance Functions and Dissipative Systems

Book chapter (2021)

Authors

J.H. van Schuppen Mathematical Physics -

Research Group

Mathematical Physics () (TU Delft)

Covariance function Dissipative system Storage function

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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.