Sensitivity Limitations for Multivariable Linear Filtering

Weller, Steven R.

doi:https://doi.org/10.1155/2007/27190

Journal of Control Science and Engineering

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Research Article | Open Access

Volume 2007 | Article ID 027190 | https://doi.org/10.1155/2007/27190

Sensitivity Limitations for Multivariable Linear Filtering

Steven R. Weller¹

Academic Editor: Shinji Hara

Received14 Aug 2006

Accepted22 Aug 2007

Published06 Feb 2008

Abstract

This paper examines fundamental limitations in performance which apply to linear filtering problems associated with multivariable systems having as many inputs as outputs. The results of this paper quantify unavoidable limitations in the sensitivity of state estimates to process and measurement disturbances, as represented by the maximum singular values of the relevant transfer matrices. These limitations result from interpolation constraints imposed by open right half-plane poles and zeros in the transfer matrices linking process noise and output noise with state estimates. Using the Poisson integral inequality, this paper shows how sensitivity limitations and tradeoffs in multivariable filtering problems are intimately related to the directionality properties of the open right half-plane poles and zeros in these transfer matrices.

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Copyright

Copyright © 2007 Steven R. Weller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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