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ISSN: 1546-9239 (Print)
ISSN: 1554-3641 (Online)
Research Article Open Access

Links between Dynamic Physical Systems and Operator Theory Issues Concerning Energy Balances and Stability

M. D.L. Sen1
  • 1 Department of Systems Engineering and Automatic Control, Faculty of Sciences, University of Basque Country Campus de Leioa, Bizkaia, Aptdo, 644 de Bilbao, 48080- Bilbao, Spain

Abstract

This study relates the properties of operators with the well- known concepts of positive realness and passivity properties in dynamic systems and their associate transfer functions. Those concepts together with very close related ones are first examined from a physical point of view. Then, they are related to hyper-stability and properties of transfer functions while the hyper-stability theorem is revisited and interpreted. Finally, the above concepts are compared to the mathematical concepts of positivity and closely related ones in operator theory in Hilbert spaces.

American Journal of Applied Sciences
Volume 1 No. 3, 2004, 248-254

DOI: https://doi.org/10.3844/ajassp.2004.248.254

Submitted On: 13 May 2005 Published On: 30 September 2004

How to Cite: Sen, M. D. (2004). Links between Dynamic Physical Systems and Operator Theory Issues Concerning Energy Balances and Stability. American Journal of Applied Sciences, 1(3), 248-254. https://doi.org/10.3844/ajassp.2004.248.254

Open AccessCopyright: © 2004 M. D.L. Sen. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Positivity
  • Passivity
  • Popov’s Inequality
  • Positive Operators
  • Hyperstability