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

Shunsuke YAMAKI
Masahide ABE

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.5    pp.1268-1273
Publication Date: 2008/05/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.5.1268
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
state-space digital filters,  L2-sensitivity,  minimization,  closed form solution,  

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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.