Ding, Steven X.; Frank, Paul M.:
Structure analysis via orthogonal functions
In: International Journal of Control, Vol. 50 (1989), No. 6, pp. 2285 - 2300
1989article/chapter in journal
TechnologyFaculty of Engineering » Engineering and Information Technology » Automatic Control and Complex Systems
Title:
Structure analysis via orthogonal functions
Author:
Ding, Steven X.UDE
GND
134302427
LSF ID
2347
ORCID
0000-0002-5149-5918ORCID iD
Other
connected with university
;
Frank, Paul M.
Year of publication:
1989

Abstract:

The use of orthogonal functions to analyse the structure of a system is investigated. Applying the definitions of observability and controllability to a system that is approximated with the help of orthogonal functions, it is shown that the concepts of the state space and the space of orthogonal functions are equivalent, provided that two weak conditions are met. This result ensures that the observability and controllability properties remain invariant under the transformation introduced by the approximation. Furthermore, new criteria to test observability and controllability are given in terms of the coefficient matrix of the orthogonal expansion. Because this test does not require the knowledge of the system matrices A, B and C, the results derived may be used for the identification of systems. It is demonstrated that all the results obtained remain true, even for an approximation with low accuracy. These properties allow the application of orthogonal functions for the analysis of systems