Closed form solutions to l 2-sensitivity minimization subject to l 2-scaling constraints for second-order state-space digital filters with real poles

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1587/transfun.E93.A.476

Closed form solutions to l ₂-sensitivity minimization subject to l ₂-scaling constraints for second-order state-space digital filters with real poles

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

This paper proposes closed form solutions to the L ₂-sensitivity minimization subject to L ₂-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of secondorder digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L ₂-sensitivity by a simple linear combination of exponential functions and formulate the L ₂-sensitivity minimization problem by a simple polynomial equation. As a result, L ₂-sensitivity is expressed in closed form, and its minimization subject to L ₂-scaling constraints is.

Original language	English
Pages (from-to)	476-487
Number of pages	12
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E93-A
Issue number	2
DOIs	https://doi.org/10.1587/transfun.E93.A.476
Publication status	Published - 2010 Feb

Keywords

Closed form solutions
Second-order digital filters with real poles
Variable transformation

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

Access to Document

10.1587/transfun.E93.A.476

Cite this

Closed form solutions to l ₂-sensitivity minimization subject to l ₂-scaling constraints for second-order state-space digital filters with real poles. / Yamaki, Shunsuke; Abe, Masahide; Kawamata, Masayuki.
In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E93-A, No. 2, 02.2010, p. 476-487.

Research output: Contribution to journal › Article › peer-review

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