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On the Absence of Limit Cycles in State-Space Digital Filters With Minimum L2-Sensitivity

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3 Author(s)
Yamaki, S. ; Tohoku Univ., Sendai ; Abe, M. ; Kawamata, M.

This brief proposes a systematic approach to synthesis of limit cycle free state-space digital filters with minimum L2-sensitivity. We synthesize the minimum L2-sensitivity realization adopting the balanced realization as an initial realization. The coordinate transformation matrix which transforms the balanced realization into the minimum L2-sensitivity realization is expressed as the product of a positive definite symmetric matrix and arbitrary orthogonal matrix. We show that the controllability and observability Gramians of the minimum L2-sensitivity realization satisfy a sufficient condition for the absence of limit cycles when we select an appropriate orthogonal matrix. As a result, the minimum L2-sensitivity realization without limit cycles can be synthesized by selecting an appropriate orthogonal matrix.

Published in:

Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:55 ,  Issue: 1 )

Date of Publication:

Jan. 2008

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