A dual frequency-selective bounded real lemma and its applications to IIR filter design
作者： H.D. Tuan , N.T. Hoang , H.Q. Ngo , H. Tuy , B. Vo
关键词: Mathematical optimization 、 Variable (mathematics) 、 Curse of dimensionality 、 Function (mathematics) 、 Lyapunov function 、 Filter design 、 Bounded function 、 Infinite impulse response 、 Dimension (vector space) 、 Mathematics
摘要: Given a transfer function H(s) of order n, the celebrated bounded real lemma characterises untractable semi-infinite programming (SIP) condition |H(jomega)|2 gesgamma 2forallomegaisinR realness (BR) by tractable semi-definite (SDP). Some recent results generalise this result for SIP 2forall|omega|gesomega frequency-selective (FSBR). The SDP characterisations are given at expense an introduced Lyapunov matrix variable dimension n x n. As result, resultant SDPs grows so quickly in respect to order, making them much less computationally and practicable. Moreover, they do not allow formulate synthesis problems as SDPs. In paper, completely new characterizations general FSBR all-pole functions is proposed. Our motivation design infinite-impulse-response (IIR) filters involving few simutaneous FS-BRs. moderate size free from variables thus address arbitrary order. Examples also provided validate effectiveness resulting formulation. Finally we raise some issues arising with practicability multi-dimensional filter problems. particular, any bilinear inequality (BMI) optimization shown be solved prescribed tolerance but issue dimensionality
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