Generalized KYP lemma: unified frequency domain inequalities with design applications
Generalized KYP lemma: unified frequency domain inequalities with design applications
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DOI：
10.1109/tac.2004.840475
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发表时间：
2005-01
影响因子：
6.8
通讯作者：
T. Iwasaki;S. Hara
中科院分区：
文献类型：
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作者：
T. Iwasaki;S. Hara
著名的Kalman-Yakubovic/spl caron/-Popov（KYP）引理建立了频域不等式（FDI）和线性矩阵不等式之间的等价性，在系统和控制理论中发挥了最基本的作用。本文首先给出了S-过程是无损耗的一个充分必要条件，并利用这个结果在频率范围和系统类两个方面推广了KYP引理，用一个定理统一了现有的各种版本.特别是，我们的结果涵盖了FDIs在有限的频率间隔连续/离散时间设置，而不是标准的无限频率范围。被认为是FDIs的一类系统不再被限制为适当的，也可以处理包括多项式在内的非适当传递函数。我们研究这种推广的影响，并开发一个适当的接口之间的基本结果和各种工程应用。具体而言，它表明，我们的结果使我们能够解决一定的一类系统设计问题的多个规格的增益/相位特性在几个频率范围内。数字滤波器和比例积分微分控制器的数值设计的例子说明了该方法。
The celebrated Kalman-Yakubovic/spl caron/-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality, and has played one of the most fundamental roles in systems and control theory. This paper first develops a necessary and sufficient condition for an S-procedure to be lossless, and uses the result to generalize the KYP lemma in two aspects-the frequency range and the class of systems-and to unify various existing versions by a single theorem. In particular, our result covers FDIs in finite frequency intervals for both continuous/discrete-time settings as opposed to the standard infinite frequency range. The class of systems for which FDIs are considered is no longer constrained to be proper, and nonproper transfer functions including polynomials can also be treated. We study implications of this generalization, and develop a proper interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. The method is illustrated by numerical design examples of digital filters and proportional-integral-derivative controllers.