Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for 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.2    pp.476-487
Publication Date: 2010/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.476
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
second-order digital filters with real poles,  L2-sensitivity,  L2-scaling constraints,  variable transformation,  closed form solutions,  

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This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-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 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, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.