Abstract: Almost in any field of science and technology some sort of stability problem can appear. Instability is certainly the most important phenomena, which should be investigated before any other aspect of reality will be attacked. The stability and energy of the system are closely related. Simple linear and nonlinear continuous and discrete systems are investigated from the energy point of view. As an alternative to the method of Lyapunov functions a conceptually different approach can be based on the idea that, in fact abstract state space energy can be measured as distance from the system equilibrium to the actual state, what is needed also for stability analysis. Thus, instead of the physical energy a metric function will be defined in a proper way. The idea is based on based on a generalization of the well known Tellegen’s principle.
Presented study deals with energy, stability and related structural properties of a relatively broad class of finite dimensional strictly causal continuous and discrete systems, which can be described in the state-space representation form. Dissipativity, instability, asymptotic stability as well as stability in the sense of Lyapunov is analyzed by a new approach based on an abstract state energy concept. The resulting energy metric function is induced by the output signal power and determines both, the structure of a digital system representation as well as the corresponding system state space topology.
A special form of physically correct internal structure of an equivalent state space representation has been derived for discrete time signals as a natural consequence of strict causality, signal energy conservation, dissipativity and state minimality requirements. New discretization approach of discrete systems based on energy preservations is presented. Results of simulation examples are shown for illustration of fundamental ideas and basic attributes of the proposed method.


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. He specialized in electronics systems and control in research institute in Prague. Since 1977 he worked as lecturer on University of West Bohemia in Plzen. He received 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 full 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, nonlinear and chaotic systems, control systems, signal processing and biomedical engineering, especially cardiopulmonary stress exercise systems.