A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters

Shunsuke YAMAKI; Masahide ABE; Masayuki KAWAMATA

doi:10.1093/ietfec/e91-a.5.1268

Regular Section

A Closed Form Solution to L₂-Sensitivity Minimization of Second-Order State-Space Digital Filters

Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA

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Keywords: state-space digital filters, L₂-sensitivity, minimization, closed form solution

JOURNAL RESTRICTED ACCESS

2008 Volume E91.A Issue 5 Pages 1268-1273

DOI https://doi.org/10.1093/ietfec/e91-a.5.1268

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Abstract

This paper proposes a closed form solution to L₂-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can express the L₂-sensitivity by a simple linear combination of exponential functions and formulate the L₂-sensitivity minimization problem by a simple polynomial equation. As a result, the L₂-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

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