The minimal state space realization for a class of fractional order transfer functions

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$The minimal state space realization for a class of fractional order transfer functions$

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Tavakoli Kakhki, M

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Type of Document: Article
DOI: 10.1137/090753048
Publisher: 2010
Abstract:
In this paper, the minimal state space realization of a fractional order transfer function is investigated in the sense of inner dimension both for commensurate and incommensurate cases. It is shown that while the traditional tools are applicable to check the minimality of a commensurate realization, there is no specific procedure to be certain about the minimality of incommensurate realizations. In this regard, the necessary and sufficient conditions are obtained for a specific class of fractional order transfer functions by which one can verify the existence of minimal realizations with inner dimension 2. Furthermore, a transformation is introduced through which all these realizations can be transformed to each other
Keywords:
Hadamard product-based transformation ; Fractional order transfer function ; Hadamard products ; Inner dimension ; Minimal realizations ; Minimal state ; Minimality ; Sufficient conditions ; Matrix algebra ; Transfer functions
Source: SIAM Journal on Control and Optimization ; Volume 48, Issue 7 , 2010 , Pages 4317-4326 ; 03630129 (ISSN)
URL: http://epubs.siam.org/doi/abs/10.1137/090753048