H₂-norm of fractional transfer functions of implicit type of the first kind

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• 作者：Mathieu Chevrié ; ^* ; ^** ; ^{mathieu.chevrie@mpsa.com" class="auth_mail" title="E-mail the corresponding author} ; Rachid Malti^* ; Christophe Farges^* ; Jocelyn Sabatier^*
• 关键词：H2-norm ; fractional order models ; stability ; recursive poles-zeros approximation
• 刊名：IFAC-PapersOnLine
• 出版年：2014
• 出版时间：2014
• 年：2014
• 卷：47
• 期：3
• 页码：2022-2027
• 全文大小：225 K

文摘

This paper studies the H₂-norm, or impulse response energy, of fractional transfer functions of implicit type. The analytical expression of the H₂-norm is first derived for an elementary fractional transfer function of the first kind with a single real pole. Series connection of such a transfer function with a pure fractional integrator and with another implicit transfer function of the first kind are then studied. Results developed in the paper are finally used to derive a criterion to evaluate the quality of an integer order approximation for an implicit type fractional order model of the first kind.