White Paper: Sensitivity Limitations for Multivariable Linear Filtering

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.

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In the present paper, we pursue a complementary route to multivariable filtering constraints, along the lines of Chen, wherein integral constraints on the maximum singular value of the sensitivity functions are obtained, see also for a multivariable extension of the classical Poisson integral inequality.The present paper is organized as follows. In the remainder of Section 1, we review the notion of directionality for zeros and poles of multivariable systems, and present some
mathematical and notational preliminaries.

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