The paper presents new rnethodology liow to decompose the higlh dimensional LTI (linear time invariant) systam with both distinct and repeated eigenvalues of the transition matrix into a set of first-order LTI models, which could be combined to achieve approximation of the original dynamics. As a tool, the Sylvester’s theorems are used to design the filter bank and parameters of the firstorder models (transition values). At the end, the practical examples are shown and the next steps of research of the decomposition theory are indicated.
A trial of analogies utilization among electrical, mechanical and information circuits is presented. The concepts of Information Power and significant proximity of the measure of information and knowledge could enable upgrading these analogies for solving important tasks from the area of Systems Engineering. This attempt seems to be attractive, as it could help in using the well-established and proved methodologies from the classical areas of electricity or mechanics.
Paper summarizes the results in the area of information physics that is a new progressively developing field of study trying to introduce basics of information variables into physics. New parameters, like wave information flow, wave information/knowledge content or wave information impedance, are first defined and then represented by wave probabilistic functions. Next, relations between newly defined parameters are used to compute information power or to build wave information circuits covering feedbacks, etc.
The paper presents the basic theory of wave probabilistic models together with their features. By introduction of the complementarity's principle between x-representation and k-representation the probability theory is completed for "structural" parameter which carries information about the changes of time series or random processes. The next feature of wave probabilistic models is the quantization principle or definition of probabilistic inclusion-exclusion rules.
The paper continues with the theory of wave probabilistic models and uses the inclusion-exclusion rule to describe quantum entanglement as a wave probabilities resonance principle. The achieved results are mathematically described and an illustrative example is shown to demonstrate the possible applications of the presented theory.