Closed Form Solutions to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters with Real Poles

Shunsuke YAMAKI
Masahide ABE

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.5    pp.966-971
Publication Date: 2010/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.966
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
state-space digital filters,  L2-sensitivity,  minimization,  closed form solutions,  

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This letter proposes closed form solutions to the L2-sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the minimum L2-sensitivity realizations can be synthesized by only solving a fourth-degree polynomial equation, which can be analytically solved.