Three lectures on dissipativeness

摘要

This paper has at least two sources. The first one is that in spite of the quasi-obvious significance of the notion - at the physical level of rigor - there exist some three mathematical terms with different definitions and senses; all of them are connected to stability and oscillations and are important and useful in the case of nonlinear systems. The second one is the strong connection of dissipativeness and passivity to the hyperstability theory as developed by V. M. Popov. The presentation aims to include definitions of these dissipativeness concepts, criteria, applications and connections between them. The text is underlined by the idea that Liapunov, dissipation, hyperstability and other inequalities are the common basis for discovering various dissipativeness properties.