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首页> 外文期刊>Mathematical Problems in Engineering >On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation X~s + A*X~(-t_1)A + B*X~(t_2)B = Q
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On the Hermitian Positive Definite Solutions of Nonlinear Matrix Equation X~s + A*X~(-t_1)A + B*X~(t_2)B = Q

机译：关于非线性矩阵方程X〜s + A * X〜（-t_1）A + B * X〜（t_2）B = Q的厄米正定解

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摘要

Nonlinear matrix equation X~s + A*X~(-t_1)A + B*X~(t_2)B = Q has many applications in engineering; control theory; dynamic programming; ladder networks; stochastic filtering; statistics and so forth. In this paper, the Hermitian positive definite solutions of nonlinear matrix equation X~s + A*X~(-t_1)A + B*X~(t_2)B = Q are considered, where Q is a Hermitian positive definite matrix, A, B are nonsingular complex matrices, s is a positive number, and 0 < ti≤1, I = 1,2. Necessary and sufficient conditions for the existence of Hermitian positive definite solutions are derived. A sufficient condition for the existence of a unique Hermitian positive definite solution is given. In addition, some necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions are presented. Finally, an iterative method is proposed to compute the maximal Hermitian positive definite solution, and numerical example is given to show the efficiency of the proposed iterative method.
机译：非线性矩阵方程X〜s + A * X〜（-t_1）A + B * X〜（t_2）B = Q在工程中有许多应用；控制理论动态编程阶梯网络；随机过滤统计资料等等。本文考虑非线性矩阵方程X〜s + A * X〜（-t_1）A + B * X〜（t_2）B = Q的Hermitian正定解，其中Q为Hermitian正定矩阵A ，B是非奇异复矩阵，s是一个正数，0

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第3期|p.1-18|共18页
  • 作者

    Aijing Liu; Guoliang Chen;

  • 作者单位

    Department of Mathematics, East China Normal University, Shanghai 200062, China,School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China;

    Department of Mathematics, East China Normal University, Shanghai 200062, China;

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