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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 second-order 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 achieved without iterative calculations.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.2 pp.476-487

- Publication Date
- 2010/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.476

- Type of Manuscript
- PAPER

- Category
- Digital Signal Processing

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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 2, pp. 476-487, February 2010, doi: 10.1587/transfun.E93.A.476.

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 second-order 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 achieved without iterative calculations.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.476/_p

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@ARTICLE{e93-a_2_476,

author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles},

year={2010},

volume={E93-A},

number={2},

pages={476-487},

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 second-order 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 achieved without iterative calculations.},

keywords={},

doi={10.1587/transfun.E93.A.476},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 476

EP - 487

AU - Shunsuke YAMAKI

AU - Masahide ABE

AU - Masayuki KAWAMATA

PY - 2010

DO - 10.1587/transfun.E93.A.476

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2010

AB - 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 second-order 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 achieved without iterative calculations.

ER -