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Journal of Mathematics
Volume 2018 (2018), Article ID 5298756, 16 pages
Research Article

On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching

Institute of Research and Development of Processes (IIDP), University of the Basque Country, Campus of Leioa, P.O. Box 48940, Leioa, Bizkaia, Spain

Correspondence should be addressed to M. De la Sen

Received 4 August 2017; Accepted 28 November 2017; Published 24 January 2018

Academic Editor: Viliam Makis

Copyright © 2018 M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivity (i.e., joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain is discussed.