Design of delta–sigma modulators via generalized Kalman–Yakubovich–Popov lemma

Li, Xianwei; Yu, Changbin; Gao, Huijun

doi:10.1016/j.automatica.2014.09.002

Cited by 21 publications

(12 citation statements)

References 24 publications

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“…s,i andῩ s,i,j similar to (30) and (31). Note thatQ(θ ),P(θ ), P s (θ ),K 1 (θ ), and K 2 (θ ) appearing in¯ (θ ),Ῡ(θ),¯ s (θ ), and ϒ s (θ ) are the linear combination ofP i ,Q i ,P s,i ,K 1,i , and K 2,i on the simplex , respectively.…”

mentioning

confidence: 78%

“…To overcome these disadvantages, Iwasaki and Hara [25] and Iwasaki et al [26] generalized the standard KYP lemma to finite frequency ranges, so that an RFDS can be directly converted into an equivalent LMI condition, which enables one to characterize RFDSs without introducing weighting functions. Based on the generalized KYP (GKYP) lemma, fruitful results have recently been developed for control synthesis with RFDSs [24], [27]- [31]. Especially, LMI approaches to feedback controller design subject to general RFDSs has been considered in [24] and [27].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, if = 0 −I −I 0 , then the RFDS in (5) characterizes the finite frequency positive realness property of the closed-loop system. Second, when the FI controller gain is restricted to be parameter-independent as in (21), one can takeK 1,i =K 1 and K 2,i = K 2 for the conditions in (30) and (31), which reduce tō = 1, . .…”

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confidence: 99%

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Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Gao

2015

IEEE Trans. Cybern.

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Based on a two-stage heuristic method, this paper is concerned with the design of robust feedback controllers with restricted frequency-domain specifications (RFDSs) for uncertain linear discrete-time systems. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the generalized Kalman-Yakubovich-Popov lemma for output feedback controller synthesis and robust performance analysis. Then a two-stage approach to output feedback controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required output feedback controller at the second stage. To improve the solvability of the synthesis method, heuristic iterative algorithms are further formulated for exploring the feedback gain and optimizing the initial FI controller at the individual stage. The effectiveness of the proposed design method is finally demonstrated by the application to active control of suspension systems.

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confidence: 78%

Section: Introductionmentioning

confidence: 99%

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Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Gao

2015

IEEE Trans. Cybern.

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“…The FIR error spectrum shaping filters have been proposed for recursive digital filters composed of cascaded second order section in [9]. In [10], the noise transfer function (NTF) is assumed to have an infinite impulse response which is converted to a minimization problem by virtue of generalized Kalman-Yakubovich-Popov (GKYP) lemma. Then, an iterative algorithm is developed to solve this minimization problem subject to quadratic matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%

Unified LMI-based design of ΔΣmodulators

Tariq

Ohno

2016

EURASIP J. Adv. Signal Process.

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Optimal finite impulse response (FIR) error feedback filters for noise shaping in modulators are designed by using weighting functions based on the system norms. We minimize the weighted norms of the quantization error in the output of a modulator, which corresponds to the minimization of the system norm. Three norms, the H 2 system norm, the H ∞ system norm, and the l 1 norm of the impulse response of the system, are adopted. The optimization problem for three types of FIR filters are evaluated by using linear matrix inequalities (LMIs) and then solved numerically via semi-definite programming. Design examples are provided to demonstrate the effectiveness of our proposed methods.

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“…Various designs for the feedback filter have been proposed. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, an FIR error feedback filter has been designed to minimize the worst case gain in the signal passband using convex optimization [5], whereas an infinite impulse response (IIR) filter using an iterative algorithm [6]. Under the whiteness assumption for the error of the uniform quantizer, an optimal FIR feedback filter that minimizes the variance of the error owing to quantization has been proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

Mean Squared Error Analysis of Quantizers With Error Feedback

Ohno

Teruyuki

Tariq

et al. 2017

IEEE Trans. Signal Process.

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A ∆Σ modulator that is often utilized to convert analog signals into digital signals can be modeled as a static uniform quantizer with an error feedback filter. In this paper, we present a rate-distortion analysis of quantizers with error feedback including the ∆Σ modulators, assuming that the error owing to overloading in the static quantizer is negligible. We demonstrate that the amplitude response of the optimal error feedback filter that minimizes the mean squared quantization error can be parameterized by one parameter. This parameterization enables us to determine the optimal error feedback filter numerically. The relationship between the number of bits used for the quantization and the achievable mean squared error can be obtained using the optimal error feedback filter. This clarifies the ratedistortion property of quantizers with error feedback. Then, ideal optimal error feedback filters are approximated by practical filters using the Yule-Walker method and the linear matrix inequality-based method. Numerical examples are provided for demonstrating our analysis and synthesis.

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Design of delta–sigma modulators via generalized Kalman–Yakubovich–Popov lemma

Cited by 21 publications

References 24 publications

Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Unified LMI-based design of ΔΣmodulators

Mean Squared Error Analysis of Quantizers With Error Feedback

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