Plenary Lecture

Dissipation Normal Forms and Further Applications of Lyapunov-Tellegen's Principle

Prof. Milan Stork
Department of Applied Electronics and Telecommunications
Faculty of Electrical Engineering
University of West Bohemia
P.O. Box 314
30614 Plzen, Czech Republic
Email: stork@kae.zcu.cz

Abstract: Almost in any field of science and technology some sort of stability problem can appear. Instability and chaos are certainly the most important phenomena which should be treated before any other aspect of reality will be attacked. Hence it is not very surprising that a broad variety of approaches to the problem of stability, instability and analysis of chaotic phenomena exists. Many of the most popular techniques in the field of stability and chaos are in a certain sense related to the work of A.M.Lyapunov and can be seen as energy oriented.
The Tellegen’s theorem is one of the well known forms of energy conservation statement in the field of electrical engineering. The most important feature of Tellegen’s approach is the fact that the energy conservation principle holds without any regard to physical nature of constituent network elements. This is the key idea of the proposed approach to problems of dissipativity and chaos.
The first situation arises if an energy function E[x(t)] of a given system is known in a mathematical form. In such example the time evolution of internal energy along any system motion can be described, and an energy monotonicity test can be used.
In the proposed lecture a physically motivated signal-system-theoretic approach, based on a generalisation of the well known Tellegen’s principle of electrical circuits will be presented
Two fundamental concepts are of crucial importance in the proposed approach. The first one is the concept of strongly non-linear power-informational interactions, and the second one is the notion of state space energy vector, inducing the system state-space topology. All computations, including numerical solutions of differential equations, were done using MATLAB.

Brief Biography of the Speaker:
Milan Stork received the M.Sc. degree in electrical engineering from the Technical University of Plzen, Czech Republic at the department of Applied electronics in 1974 and Ph.D. degree in automatic control systems at the Czech Technical University in Prague in 1985. In 1997, he became as Associate Professor and in 2007 professor at the Department of Applied Electronics and Telecommunication, faculty of electrical engineering on University of West Bohemia in Plzen, Czech Republic. He has numerous journal and conference publications. He is member of editorial board magazine "Physician and Technology". His research interest includes analog/digital linear and nonlinear systems, control systems, signal processing and biomedical engineering, especially cardiopulmonary stress tests systems.