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Structure analysis via orthogonal functions -new results for observability and controllability properties

By: Frank, P.M.; Ding, X.;

1989 / IEEE

Description

This item was taken from the IEEE Periodical ' Structure analysis via orthogonal functions -new results for observability and controllability properties ' This paper investigates the use of orthogonal functions to analyze the structure of dynamic systems. It is first shown that the concepts of observability and controllability of the state-space and the space of orthogonal functions are equivalent, provided that two weak conditions are met. This result ensures the invariance of observability and controllability 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. It is shown 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 the system structure. Several examples are included to illustrate the applicability of the proposed criteria.