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Digraph-building method for finding a set of minimal realizations of 2-D dynamic systems

Markowski K. A., Hryniów K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 5

589--597

This paper presents a digraph-building method designed to find the determination of realization of two-dimensional dynamic system. The main differences between the method proposed and other state-of-the-art solutions used include finding a set of realizations (belonging to a defined class) instead of only one realization, and the fact that obtained realizations have minimal size of state matrices. In the article, the proposed method is described, compared to state-of-the-art methods and illustrated with numerical examples. To the best of authors’ knowledge, the method shown in the paper is superior to all other state-of-the-art solutions both in terms of number of solutions and their matrix size. Additionally, MATLAB function for determination of realization based on the set of state matrices is included.

Computation of realizations composed of dynamic and static parts of improper transfer matrices

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 1

23-25

The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the computation of a minimal dynamical-static realization for a given improper transfer matrix is proposed and illustrated by a numerical example.