张娟导师主页
基本信息
姓名: 张娟
职称: 副教授
单位电话:
电子信箱: zhangjuan@xtu.edu.cn
办公室: 数学院II办公楼411
个人主页:
http://yjs.xtu.edu.cn/gmis/dsgl/dsfc.aspx?id=46F00F41C8378085EB82ACBB2460CF5A
个人简介



 

张娟,女,博士,副教授,博士生导师。

2015年,荣获首届全国高校数学微课程教学设计竞赛华中赛区二等奖、湘潭大学青年教师教学比赛三等奖、湘潭大学优秀研究生班主任。2013年,荣获湘潭大学第十八届研究生校长奖优秀奖。2012年,荣获博士研究生国家奖学金。2011年,荣获宝钢优秀学生特等奖、 湖南省优秀硕士论文奖。

 

主要从事数值代数、矩阵理论及其应用,线性控制等方面的研究。在国内外重要学术期刊 Linear Algebra and its Applications Journal of Inequalities and ApplicationsInternational Journal of ControlAsian Journal of Control等杂志上发表SCI论文30篇。现主持国家自然科学基金面上项目1项、国家自然科学基金青年项目1项、湖南省自然科学基金青年项目1项、湘潭大学博士科研启动项目1项,主持完成博士后科学基金面上项目一等资助1项、湖南省教育厅一般项目1,参与国家自然科学基金项目3项、多项省部级项目的研究。

  

主讲《高等代数》、《高等数学》、《线性代数》等本科生课程。

 

研究方向



矩阵方程解的性质和解的估计

高效稳定的数值算法

特殊矩阵的性质与判定

矩阵降阶处理

 

欢迎咨询报考研究生!

获奖情况



2015年,首届全国高校数学微课程教学设计竞赛华中赛区二等奖

2015年,湘潭大学青年教师教学比赛三等奖

2015年,湘潭大学优秀研究生班主任

2012年,博士研究生国家奖学金

2011年,宝钢优秀学生特等奖    

2011年,湖南省优秀硕士论文奖 

2011年,湖南省高校优秀研究生

2012年,湖南省普通高校优秀学生党员 

2012年,湖南省第五届研究生创新论坛优秀论文一等奖 

2010年,湖南省第三届研究生创新论坛优秀论文一等奖 

2013年,湘潭大学第十八届研究生校长奖优秀奖

2012年,湘潭大学三好研究生标兵

 

科研项目



主持项目:

2018.01--2021.12 国家自然科学基金面上项目:基于Riccati方程和LMI的控制系统鲁棒稳定性研究

2015.01--2017.12 国家自然科学基金青年项目:控制系统的约束矩阵方程及其高效数值算法

2017.06--2019.06 湖南省自然科学基金青年项目:控制系统中Riccati矩阵方程的数学分析及其高效算法研究

2015.09--2017.09  博士后科学基金面上资助一等资助项目:约束矩阵方程及其迭代算法

2015.09--2017.09  湖南省教育厅一般项目:线性系统的稳定性分析及其矩阵降阶

2013.09--2019.09 湘潭大学博士科研启动项目:控制系统中的矩阵方程的约束解及其数值算法

2011.09--2013.06 湖南省研究生创新基金项目:控制理论中的某些矩阵方程的解及其数值算法

 

 参与项目:

2011.01--2013.12,国家自然科学基金青年项目:高相对精度的矩阵分解与数值计算方法

2010.01--2012.12,国家自然科学基金面上项目:大型特殊矩阵的降阶和特征值分布

2007.01--2008.12,国家自然科学基金面上项目:大型特殊矩阵的降低规模、保结构及其高效算法

2012.01--2015.12,湖南省教育厅重点项目:耦合系统中大型矩阵方程的约束解及其高效数值算法

2015.01--2017.12,湖南省自然科学基金面上项目:大系统控制中的大型特殊矩阵及其降低规模处理

2009.01--2012.12,湖南省自然科学基金重点项目: 几类特殊矩阵及其Schur补和大型矩阵计算的降阶处理

2007.01--2009.12,湖南省教育厅重点项目:广义控制系统的相关稳定性研究

 

论文专著



[1].Juan Zhang and Jianzhou Liu, The matrix bounds and fixed-point iteration for the solution of the discrete algebraic Riccati equation, IMA Journal of Mathematical Control and Information, 2018, online (SCI 三区).

[2].Jianzhou Liu,Juan Zhang, Lixin zhou and Gen Tu,The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications, Applied Mathematics and Computation, 320, 251-263, 2018 (SCI 二区).

[3].Juan Zhang, Jianzhou Liu and Hao Huang, Lower eigenvalue bounds on summation for the solution of the Lyapunov matrix differential equation, Asian Journal of Control, 19(1), 382-390, 2017 (SCI 三区).

[4].Juan Zhang, Jianzhou Liu and Yalin Zha, The improved eigenvalue bounds for the solution of the discrete algebraic Riccati equation, IMA Journal of Mathematical Control and Information,  34(3), 851-870, 2017 (SCI 三区).

[5].Juan Zhang, Jianzhou Liu and Quanbing Li, Lower bounds on eigenvalue summation for the solution of the Lyapunov matrix differential equation, IMA Journal of Mathematical Control and Information, 34(3), 987-998, 2017 (SCI 三区).

[6].Guangqi Li, Jianzhou Liu and Juan Zhang, The disc theorem for the Schur complement of two class submatrices with r-diagonally dominant properties, Numerical Mathematics: Theory, Methods and Applications, 10(1), 84-97, 2017 (SCI 四区).

[7].Jianzhou Liu, Li Wang and Juan Zhang, New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation, International Journal of Control, 90(11), 2326-2337, 2017 (SCI 二区).

[8].Jianzhou Liu, Li Wang and Juan Zhang, The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control, IMA Journal of Mathematical Control and Information, 34(1), 1135-1156, 2017 (SCI 三区).

[9].Jianzhou Liu, Yanpei Wang and Juan Zhang, New upper matrix bounds with power form for the solution of the continuous coupled algebraic Riccati matrix equation, Asian Journal of Control, 19(2), 730-747, 2017 (SCI 三区).

[10].Juan Zhang and Jianzhou Liu, New upper and lower bounds, the iteration algorithm for the solution of the discrete algebraic Riccati equation, Advances in Difference Equations, 2015:313, 17 pages, doi: 10.1186/s13662-015-0649-6, 2015 (SCI 二区).

[11].Jiang Kai, Juan Zhang and Qin Liang, Self-assembly of asymmetrically interacting ABC star triblock copolymer melts, The Journal of Physical Chemistry B, 43(19), 14551-14562, 2015 (SCI 二区).

[12].Jianzhou Liu and Juan Zhang, New upper and lower eigenvalue bounds for the solution of the continuous algebraic Riccati equation, Asian Journal of Control, 16(1), 284-291, 2014 (SCI 三区).

[13].Juan Zhang and Jianzhou Liu, The improved upper solution bounds of the continuous coupled algebraic Riccati matrix equation, International Journal of Control, Automation, and Systems, 11(4), 852-858, 2013 (SCI 三区).

[14].Juan Zhang, Jianzhou Liu and Gen Tu, The improved disc theorems for the Schur complements of diagonally dominant matrices, Journal of Inequalities and Applications, 2013:2, 16 pages, doi:10.1186/1029-242X-2013-2, 2013 (SCI 二区).

[15].Juan Zhang and Jianzhou Liu, Lower solution bounds of the continuous coupled algebraic Riccati matrix equation, International Journal of Control, Automation, and Systems, 10(6), 1273-1278, 2012 (SCI 三区).

[16].Juan Zhang and Jianzhou Liu, New matrix bounds, an existence uniqueness and a fixed-point iterative algorithm for the solution of the unified coupled algebraic Riccati equation, International Journal of Computer Mathematics, 89, 527-542, 2012 (SCI 三区).

[17].Jianzhou Liu, Juan Zhang and Yu Liu, The Schur complement of strictly doubly diagonally dominant matrices and its application, Linear Algebra and its Applications, 437(1), 168-183, 2012 (SCI 二区).

[18].Jianzhou Liu and Juan Zhang, New upper matrix bounds of the solution for perturbed continuous coupled algebraic Riccati matrix equation, International Journal of Control, Automation, and Systems, 10(6), 1254-1259, 2012 (SCI 三区).

[19].Juan Zhang and Jianzhou Liu, New lower solution bounds for the continuous algebraic Riccati equation, Electronic Journal of Linear Algebra, 22, 191-202, 2011 (SCI 三区).

[20].Jianzhou Liu and Juan Zhang, Upper solution bounds of the continuous coupled algebraic Riccati matrix equation, International Journal of Control, 84(4), 726-736, 2011 (SCI 二区).

[21].Jianzhou Liu and Juan Zhang, The existence uniqueness and the fixed iterative algorithm of the solution for the discrete coupled algebraic Riccati equation, International Journal of Control, 84(8), 1430-1441, 2011 (SCI 二区).

[22].Jianzhou Liu and Juan Zhang, The open question of the relation between square matrix’s eigenvalues and its similarity matrix’s singular values in linear discrete system, International Journal of Control, Automation, and Systems, 9(6), 1235-1241, 2011 (SCI 三区).

[23].Jianzhou Liu, Juan Zhang and Yu Liu, New solution bounds for the continuous algebraic Riccati equation, Journal of the Franklin Institute, 348, 2128-2141, 2011 (SCI 二区).

[24].Jianzhou Liu and Juan Zhang, Bounds for the eigenvalues of the continuous algebraic Riccati equation, International Journal of Systems Science, 42(10), 1747-1753, 2011 (SCI 二区).

[25].Juan Zhang and Jianzhou Liu, New estimates for the solution of the Lyapunov matrix  differential equation, Electronic Journal of Linear Algebra, 20, 6-19, 2010 (SCI 三区).

[26].Juan Zhang and Jianzhou Liu, Matrix bounds for the solution of the continuous algebraic Riccati equation, Mathematical Problems in Engineering,Volume 2010, Article ID 819064, 15 pages, doi:10.1155/2010/819064, 2010 (SCI 三区).

[27].Jianzhou Liu, Juan Zhang and Yu Liu, A new upper bound for the eigenvalues of the continuous algebraic Riccati equation, Electronic Journal of Linear Algebra, 20, 314-321, 2010 (SCI 三区).

[28].Jianzhou Liu, Zejun Huang and Juan Zhang, The dominant degree and disc theorem for the Schur complement of matrix, Applied Mathematics and Computation, 215, 4055-4066, 2010 (SCI 二区).

[29].Jianzhou Liu and Juan Zhang, New trace bounds for the product of two matrices and their applications in the algebraic Riccati equation, Journal of Inequalities and Applications, vol. 2009, Article ID 620758, 18 pages, 2009. doi:10.1155/2009/620758 (SCI 二区).

[30].Jianzhou Liu, Juan Zhang and Yu Liu, Trace inequalities for matrix products and trace bounds for the solution of the algebraic Riccati equations, Journal of Inequalities and Applications, vol. 2009, Article ID 101085, 17 pages, 2009. doi:10.1155/2009/101085 (SCI 二区).