非线性矩阵方程的厄米正定解

2011 International Conference on System science, Engineering design and Manufacturing informatization Pub Date : 2011-11-18 DOI:10.1109/ICSSEM.2011.6081228

Qingchun Li, Panpan Liu

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引用次数: 1

摘要

本文讨论了非线性矩阵方程X + A*X−qA = Q和X−A*X−qA = Q的厄米正定解，其中Q∈(0,1)。导出了这些方程存在厄密正定解的几个充分条件。给出了X + A*X−qA = Q有唯一厄米正定解的充分条件。最后讨论了X−A*X−qA = Q的微扰分析。

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On Hermitian positive definite solutions of nonlinear matrix equation

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equations X + A*X^−qA = Q and X − A*X^−qA = Q are discussed where q∈(0,1]. Some sufficient conditions for the existence of Hermitian positive definite solutions for these equations are derived. A sufficient condition for X + A*X^−qA = Q is given to have a unique Hermitian positive definite solution. The perturbation analysis for X − A*X^−qA = Q is discussed at last.

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2011 International Conference on System science, Engineering design and Manufacturing informatization

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