On two generalisations of the final value theorem: scientific relevance, first applications, and physical foundations

Abstract

The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem.

Keywords:

• control
• linear systems
• queueing theory
• Laplace transform
• irrational functions
• noninteger integration
• ergodic systems

Acknowledgements

The authors are grateful to Professor Menachem Krichevsky for the example of the frequency-dependent inductor in Section 3.4.2.

Notes

1. J. Walraevens is a Postdoctoral Fellow with the Fund for Scientific Research, Flanders (F.W.O.-Vlaanderen), Belgium.