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Some conceptual links between dynamic physical systems and operator theory issues concerning energy balances and stability. (English) Zbl 1140.93473
Summary: 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.

MSC:
93D05Lyapunov and other classical stabilities of control systems
47N70Applications of operator theory in systems theory, circuits, and control theory
93B28Operator-theoretic methods in systems theory