Stability margin optimization via interpolation and conformal mappings

Cockburn J.C.; Sidar Y.

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Stability margin optimization via interpolation and conformal mappings

机译：通过插值和保形映射优化稳定性裕度

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Many interesting problems of robust stabilization can be solved using the complex function theoretic approach of Khargonekar and Tannenbaum (1985). This method is based on the construction of a conformal mapping which reduces the original robust stabilization problem to a Nevanlinna-Pick interpolation problem. The main difficulty of this approach lies in the construction the conformal mapping. The authors present a new numerical algorithm to construct such conformal mappings. Then they demonstrate its effectiveness in the synthesis of optimal gain-phase margin controllers.

机译：使用Khargonekar和Tannenbaum（1985）的复函数理论方法可以解决鲁棒稳定的许多有趣问题。此方法基于共形映射的构造，该共形映射将原始的鲁棒稳定问题简化为Nevanlinna-Pick插值问题。这种方法的主要困难在于构造共形映射。作者提出了一种新的数值算法来构造这种共形映射。然后他们证明了其在最佳增益相位裕量控制器综合中的有效性。

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《IEEE Transactions on Automatic Control》 |1995年第6期|P.1066-1070|共5页
作者
Cockburn J.C.; Sidar Y.;
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1. Stability margin optimization via interpolation and conformalmappings [J] . Cockburn J.C., Sidar Y., Tannenbaum A.R. IEEE Transactions on Automatic Control . 1995,第6期

机译：通过插值和保形映射优化稳定性裕度
2. Conformal Mapping and Periodic Cubic Spline Interpolation [J] . Ali H. M. Murid, Lee Khiy Wei, Yeak Su Hoe Matematika . 2014,第0期

机译：共形映射和周期三次样条插值
3. Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions [J] . Boyd J.P., Yu F. Journal of Computational Physics . 2011,第4期

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4. Mapping of Nyquist/popov theta-stability margins into parameter space [C] . Tilman Bunte IFAC ROCOND symposium on robust control design . 2000

机译：奈奎斯特/波波夫θ稳定裕度到参数空间的映射
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7. Discrete Riemann–Hilbert problems, interpolation of simply closed curves, and numerical conformal mapping [O] . Wegmann Rudolf 1988

机译：离散黎曼–希尔伯特问题，简单闭合曲线的内插和数值共形映射

Stability margin optimization via interpolation and conformal mappings

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