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

Article type: Research Article

Authors: De la Sen, M.

Affiliations: 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, e-mail: [email protected]

Abstract: This paper relates 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 with hyperstability and properties of transfer functions while the hyperstability 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.

Keywords: positivity, passivity, Popov's inequality, positive operators, hyperstability

Journal: Informatica, vol. 16, no. 3, pp. 395-406, 2005