The Experts below are selected from a list of 29301 Experts worldwide ranked by ideXlab platform
Keung Kwan - One of the best experts on this subject based on the ideXlab platform.
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IIR Digital Filter Design With New Stability Constraint Based on Argument Principle
IEEE Transactions on Circuits and Systems I: Regular Papers, 2009Co-Authors: Aimin Jiang, Keung KwanAbstract:This paper presents a weighted least squares (WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative second-order cone programming (SOCP) method is employed to solve the design problem, such that either linear or second-order cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the Argument Principle (AP) of complex analysis. As compared with other frequency-domain stability constraints, the AP-based stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then combined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method.
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APCCAS - Unconstrained IIR filter design method using Argument Principle based stability criterion
APCCAS 2008 - 2008 IEEE Asia Pacific Conference on Circuits and Systems, 2008Co-Authors: Aimin Jiang, Keung KwanAbstract:In this paper, we propose an unconstrained IIR digital filter design method in the weighted least-squares (WLS) sense. Unlike some other design methods which utilize approximation techniques to simplify the nonlinear approximation error functions, this method expresses the design problem strictly, and utilizes the general-purpose optimization algorithms to find the minimum point. In order to guarantee the stability of designed filters, a stability criterion is developed from the Argument Principle of complex analysis. Unlike other frequency-domain stability criteria, it is both sufficient and necessary. Two examples are also presented to demonstrate the effectiveness of the proposed method.
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ISCAS - IIR Digital Filter Design with Novel Stability Criterion Based on Argument Principle
2007 IEEE International Symposium on Circuits and Systems, 2007Co-Authors: Aimin Jiang, Keung KwanAbstract:A method for designing IIR digital filters with a novel stability criterion based on the Argument Principle is proposed in this paper. Unlike the stability criteria used in some design algorithms, this stability condition is both sufficient and necessary. In the paper, the weighted least-squares (WLS) design of IIR filters is first formulated as an iterative quadratic programming (QP) problem without any constraint. Then the stability criterion is incorporated in the quadratic form at each iteration. Two examples are presented to illustrate the effectiveness of the proposed approach.
Aimin Jiang - One of the best experts on this subject based on the ideXlab platform.
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IIR Digital Filter Design With New Stability Constraint Based on Argument Principle
IEEE Transactions on Circuits and Systems I: Regular Papers, 2009Co-Authors: Aimin Jiang, Keung KwanAbstract:This paper presents a weighted least squares (WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative second-order cone programming (SOCP) method is employed to solve the design problem, such that either linear or second-order cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the Argument Principle (AP) of complex analysis. As compared with other frequency-domain stability constraints, the AP-based stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then combined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method.
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unconstrained iir filter design method using Argument Principle based stability criterion
Asia Pacific Conference on Circuits and Systems, 2008Co-Authors: Aimin Jiang, H K KwanAbstract:In this paper, we propose an unconstrained IIR digital filter design method in the weighted least-squares (WLS) sense. Unlike some other design methods which utilize approximation techniques to simplify the nonlinear approximation error functions, this method expresses the design problem strictly, and utilizes the general-purpose optimization algorithms to find the minimum point. In order to guarantee the stability of designed filters, a stability criterion is developed from the Argument Principle of complex analysis. Unlike other frequency-domain stability criteria, it is both sufficient and necessary. Two examples are also presented to demonstrate the effectiveness of the proposed method.
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APCCAS - Unconstrained IIR filter design method using Argument Principle based stability criterion
APCCAS 2008 - 2008 IEEE Asia Pacific Conference on Circuits and Systems, 2008Co-Authors: Aimin Jiang, Keung KwanAbstract:In this paper, we propose an unconstrained IIR digital filter design method in the weighted least-squares (WLS) sense. Unlike some other design methods which utilize approximation techniques to simplify the nonlinear approximation error functions, this method expresses the design problem strictly, and utilizes the general-purpose optimization algorithms to find the minimum point. In order to guarantee the stability of designed filters, a stability criterion is developed from the Argument Principle of complex analysis. Unlike other frequency-domain stability criteria, it is both sufficient and necessary. Two examples are also presented to demonstrate the effectiveness of the proposed method.
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iir digital filter design with novel stability criterion based on Argument Principle
International Symposium on Circuits and Systems, 2007Co-Authors: Aimin Jiang, H K KwanAbstract:A method for designing IIR digital filters with a novel stability criterion based on the Argument Principle is proposed in this paper. Unlike the stability criteria used in some design algorithms, this stability condition is both sufficient and necessary. In the paper, the weighted least-squares (WLS) design of IIR filters is first formulated as an iterative quadratic programming (QP) problem without any constraint. Then the stability criterion is incorporated in the quadratic form at each iteration. Two examples are presented to illustrate the effectiveness of the proposed approach.
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ISCAS - IIR Digital Filter Design with Novel Stability Criterion Based on Argument Principle
2007 IEEE International Symposium on Circuits and Systems, 2007Co-Authors: Aimin Jiang, Keung KwanAbstract:A method for designing IIR digital filters with a novel stability criterion based on the Argument Principle is proposed in this paper. Unlike the stability criteria used in some design algorithms, this stability condition is both sufficient and necessary. In the paper, the weighted least-squares (WLS) design of IIR filters is first formulated as an iterative quadratic programming (QP) problem without any constraint. Then the stability criterion is incorporated in the quadratic form at each iteration. Two examples are presented to illustrate the effectiveness of the proposed approach.
Bassam Bamieh - One of the best experts on this subject based on the ideXlab platform.
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An Extension of the Argument Principle and Nyquist Criterion to a Class of Systems With Unbounded Generators
IEEE Transactions on Automatic Control, 2008Co-Authors: Makan Fardad, Bassam BamiehAbstract:The Nyquist stability criterion is generalized to systems where the open-loop system has infinite-dimensional input and output spaces and an unbounded infinitesimal generator. The infinitesimal generator is assumed to be a sectorial operator with trace-class resolvent. The main result is obtained through use of the perturbation determinant and an extension of the Argument Principle to infinitesimal generators with trace-class resolvents.
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An Extension of the Argument Principle and Nyquist Criterion to Systems with Unbounded Generators
2006Co-Authors: Makan Fardad, Bassam BamiehAbstract:Abstract : The Nyquist Stability Criterion is generalized to systems where the (open-loop) system has infinite-dimensional input/output spaces and a (possibly) unbounded infinitesimal generator. This is done through use of the perturbation determinant and an extension of the Argument Principle to infinitesimal generators with trace-class resolvent.
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The Nyquist Stability Criterion For A Class Of Spatially Periodic Systems
Proceedings of the 44th IEEE Conference on Decision and Control, 1Co-Authors: Makan Fardad, Bassam BamiehAbstract:The Nyquist stability criterion is extended to a class of spatially periodic systems with spatially distributed inputs and outputs. It is demonstrated that the exponential stability of this class of systems can be guaranteed by checking the Nyquist stability criterion for a family of finite-dimensional systems. In order to show this result, a new version of the Argument Principle is derived that is applicable to systems with infinite-dimensional input/output spaces and unbounded system operators.
Li Qiu - One of the best experts on this subject based on the ideXlab platform.
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extended Argument Principle and integral design constraints part i a unified formula for classical results
Conference on Decision and Control, 2000Co-Authors: Jie Chen, G Chen, Zhiyuan Ren, Li QiuAbstract:We study Bode and Poisson type integral relations. We focus on a link between the well-known Argument Principle and Bode and Poisson integrals, which have been unnoticed previously. We show how various integral constraints may be unified under an extended version of the Argument Principle. This enables us to derive the classical Bode and Poisson integral relations in a simple manner, and further to discover new integral formulas of significance for an analysis of control design limitation and tradeoff.
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Extended Argument Principle and integral design constraints. II. New integral relations
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 1Co-Authors: G Chen, Jie Chen, Li QiuAbstract:For pt.1 see Proc. 39th IEEE Conf. Decision Contr., p.4984-89 (2000). This paper studies performance limitation and design tradeoff issues in the analysis and design of linear time-invariant, single-input single-output feedback control systems. We develop a number of integral constraints, which extend the classical Bode/Poisson sensitivity and complementary sensitivity integrals. The new integral relations lead to new insights into the study of fundamental limitation and design tradeoff issues, and together with the classical results, enable a more refined and more informative performance analysis.
Lawrence C Paulson - One of the best experts on this subject based on the ideXlab platform.
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Evaluating Winding Numbers and Counting Complex Roots Through Cauchy Indices in Isabelle/HOL
Journal of Automated Reasoning, 2020Co-Authors: Lawrence C PaulsonAbstract:In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover, and provide a tactic to evaluate winding numbers through Cauchy indices. By further combining this approximation with the Argument Principle, we are able to make use of remainder sequences to effectively count the number of complex roots of a polynomial within some domains, such as a rectangular box and a half-plane.
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evaluating winding numbers and counting complex roots through cauchy indices in isabelle hol
Journal of Automated Reasoning, 2020Co-Authors: Lawrence C PaulsonAbstract:In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover, and provide a tactic to evaluate winding numbers through Cauchy indices. By further combining this approximation with the Argument Principle, we are able to make use of remainder sequences to effectively count the number of complex roots of a polynomial within some domains, such as a rectangular box and a half-plane.
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Evaluating Winding Numbers through Cauchy Indices in Isabelle/HOL
arXiv: Logic in Computer Science, 2018Co-Authors: Lawrence C PaulsonAbstract:In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover, and provide a tactic to evaluate winding numbers through Cauchy indices. By further combining this approximation with the Argument Principle, we are able to make use of remainder sequences to effectively count the number of complex roots of a polynomial within some domains, such as a rectangle box and a half-plane.
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a formal proof of cauchy s residue theorem
Interactive Theorem Proving, 2016Co-Authors: Wenda Li, Lawrence C PaulsonAbstract:We present a formalization of Cauchy’s residue theorem and two of its corollaries: the Argument Principle and Rouche’s theorem. These results have applications to verify algorithms in computer algebra and demonstrate Isabelle/HOL’s complex analysis library.
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ITP - A Formal Proof of Cauchy’s Residue Theorem
Interactive Theorem Proving, 2016Co-Authors: Wenda Li, Lawrence C PaulsonAbstract:We present a formalization of Cauchy’s residue theorem and two of its corollaries: the Argument Principle and Rouche’s theorem. These results have applications to verify algorithms in computer algebra and demonstrate Isabelle/HOL’s complex analysis library.