A theory of passive linear systems with no assumptions
Timothy H. Hughes
TL;DR
This paper establishes comprehensive theorems characterizing passivity in general linear systems, including conditions for passivity and an extension of the positive-real lemma to systems with uncontrollable or unobservable states.
Contribution
It introduces necessary and sufficient conditions for passivity in high-order linear systems and extends the positive-real lemma to broader classes of systems.
Findings
Provides necessary and sufficient passivity conditions for general linear systems
Extends the positive-real lemma to uncontrollable and unobservable systems
Lays theoretical foundation for analyzing passive behavior in complex systems
Abstract
We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be passive. Part 2 extends the positive-real lemma to include uncontrollable and unobservable state-space systems.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.