On the Kalman-Yakubovich-Popov Lemma for Positive Systems
On the Kalman-Yakubovich-Popov Lemma for Positive Systems
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关于正系统的卡尔曼-雅库博维奇-波波夫引理
DOI：
10.1109/tac.2015.2465571
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发表时间：
2012
影响因子：
6.8
通讯作者：
A. Rantzer
中科院分区：
文献类型：
--
作者：
A. Rantzer
导出了正系统的一个推广的Kalman-Yakubovich-Popov（KYP）引理。与早期版本相比，主要区别在于处理了非严格不等式。矩阵假设的限制性也较小。此外，一个新的等价性，而不是半定规划的线性规划。作为对KYP引理的补充，我们还证明了一个对角线上有m个非零元素的对称Metzler矩阵是半负定的当且仅当它可以写成m个半负定矩阵的和，每个矩阵只有4个非零元素。这在大规模优化的上下文中是有用的。
An extended Kalman-Yakubovich-Popov (KYP) Lemma for positive systems is derived. The main difference compared to earlier versions is that non-strict inequalities are treated. Matrix assumptions are also less restrictive. Moreover, a new equivalence is introduced in terms of linear programming rather than semi-definite programming. As a complement to the KYP lemma, it is also proved that a symmetric Metzler matrix with m nonzero entries above the diagonal is negative semi-definite if and only if it can be written as a sum of m negative semi-definite matrices, each of which has only four nonzero entries. This is useful in the context large-scale optimization.
影响因子：
6.8
作者：
T. Iwasaki;S. Hara
通讯作者：
T. Iwasaki;S. Hara