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分块矩阵的正定性准则及其应用(英文) 被引量：1

A Criterion for the Positive Definiteness of A Block-Matrix and Its Application
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摘要 本文给出了 3× 3分块矩阵的一个正定性判定准则 ,应用这个准则 ,给出了矩阵方程 (ATXB ,BT×B)=(C ,D) A criterion for the positive definiteness of symmertic 3×3 block-matrix A is presented.Applying the criterion ,we derive the necessary and sufficient conditions for that the matrix equation ( A TXA,B TXB)=(C,D ) has positive definite solution.The expression of the general solution is given.
作者 刘向华
机构地区 株洲师专数学系
出处 《数学理论与应用》 2001年第3期122-128,共7页 Mathematical Theory and Applications
关键词 分块矩阵 正定性 判定准则 矩阵方程 正定解 充分条件 通式
分类号 O151.21 [理学—基础数学]
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同被引文献17

  • 1Cheng P, Deng F Q. Global exponential stability of impulsive stochastic functional differential systems[J]. Statistics and Probability Letters, 2010, 80(23/24): 1854- 1862.
  • 2Zhang H, Guan Z H, Feng G. Reliable dissipative control for stochastic impulsive systems[J]. Automatica, 2008, 44(4): 1004-1010.
  • 3Wu F K, Hu S G, Huang C M. Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay[J]. Systems Control Letters, 2010, 59(3/4): 195-202.
  • 4Peng S, Jia B. Some criteria on pth moment stability of impulsive stochastic functional differential equations[J]. Siatishcs and Probability Letters, 2010, 80(13/14): 1085- 1092.
  • 5Liu B, Marquez H J. Uniform stability of discrete delay systems and synchronization of discrete delay dynamical networks via razumikhin technique[J]. IEEE Trans on Circuits and Systems, 2008, 55(9): 2795-2805.
  • 6Liu J, Liu X Z, Xie W C. Impulsive stabilization of stochastic functional differential equations[J]. Applied Mathematics Letters, 2011, 24(3): 264-269.
  • 7Xu L G, Xu D Y. Mean square exponential stability of impulsive control stochastic systems with time-varying delay[J]. Physics Letters A, 2009, 373(3): 328-333.
  • 8Rakkiyappan R, Balasubramaniam P, Cao J D. Global exponential stability results for neutral-type impulsive neural networks[J]. Nonlinear Analysis: Real World Applications, 2010, 11(1): 122-130.
  • 9Samidurai R, Anthoni S, Balachandran K. Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays[J]. Nonlinear Analysis: Hybrid Systems, 2010, 4(1): 103-112.
  • 10Bao J H, Hou Z T, Wang F X. Exponential stability in mean square of impulsive stochastic difference equations with continuous time[J]. Applied Mathematics Letters, 2009, 22(5): 749-753.

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数学理论与应用
2001年 第3期

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