张娟，博士，教授，博导，湖南省青年骨干教师培养对象，数学与应用数学系主任。2018年赴新加坡国立大学国家公派访问1年。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、博士后科学基金面上项目一等资助1项、湖南省自科基金青年项目1项、湖南省教育厅优秀青年项目1项、湖南省教改项目1项。

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 Automatica、Journal of Computational Physics、Journal of Computational and Applied Mathematics、Linear Algebra and its Applications、Linear and Multilinear Algebra、Computational and Applied Mathematics、Journal of Inequalities and Applications、 Journal of the Franklin Institute、International Journal of Control、Asian Journal of Control等杂志上发表SCI论文40篇。

2020年，荣获湘潭大学优秀班主任、湘潭大学优秀党员、指导研究生获湘潭大学第二十五届研究生校长奖特等奖。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，湖南省优秀党员，博士研究生国家奖学金。2011年，宝钢优秀学生特等奖、湖南省优秀硕士论文、湖南省优秀研究生、湖南省普通高校优秀学生党员。

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！

2020年，湘潭大学第二十五届研究生校长奖特等奖

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

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

2018.09--2020.12，  湖南省教育厅优秀青年项目：矩阵不等式在Riccati矩阵方程中的应用

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

2019.09--2022.09， 湖南省教改项目：“双一流”背景下地方本科院校数学与应用数学专业培养计划探索与实践

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：

2016.01--2019.12，国家自然科学基金面上项目：复杂系统中的非线性矩阵方程及降阶处理

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

[1].Juan Zhang and Shifeng Li, The structure-preserving doubling algorithm and convergence analysis for a nonlinear matrix equation, Automatica, 113, 108822, 2020 (SCI).

[2].Jianzhou Liu,Juan Zhang and Quanbing Li, Upper and lower eigenvalue summation bounds of the Lyapunov matrix differential equation and the application in a class time-varying nonlinear system, International Journal of Control, 93(5), 1115-1126, 2020(SCI).

[3].Juan Zhang, Huihui Kang and Fangyuan Tan, Two-parameters numerical methods of the non-symmetric algebraic Riccati equation, Journal of Computational and Applied Mathematics, 378, 112933, 2020 (SCI).

[4].Ze Chen, Juan Zhang, Kenneth L. Ho, Haizhao Yang, Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization, Journal of Computational Physics, 412, 109427，2020 (SCI).

[5].Jianzhou Liu, Juan Zhang and Fangfang Luo, Newton's method for the positive solution of the coupled algebraic Riccati equation applied to automatic control, Computational and Applied Mathematics, 39: 113, 2020 (SCI).

[6].Juan Zhang and Huihui Kang, The generalized modified Hermitian and skew-Hermitian splitting method for the generalized Lyapunov equation,  International Journal of Control, Automation and Systems, 2020, online (SCI).

[7].Juan Zhang and Shifeng Li, The structure-preserving doubling numerical algorithm of the continuous coupled algebraic Riccati equation, International Journal of Control, Automation and Systems, 18(7), 1641-1650, 2020 (SCI).

[8].Jianzhou Liu, Juan Zhang and Hao Huang, The eigenvalue product bounds of the Lyapunov matrix differential equation and the stability of a class of time-varying nonlinear system, Journal of Inequalities and Applications, 2019:172, 18 pages, https://doi.org/10.1186/s13660-019-2119-2, 2019 (SCI ).

[9].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, 36, 681-699, 2019 (SCI).

[10].Juan Zhang and Fangyuan Tan, Numerical methods for the minimal non-negative solution of the non-symmetric coupled algebraic Riccati equation, Asian Journal of Control, 2019, online (SCI).

[11].Juan Zhang and Shifeng Li, On the Hermitian positive denite solution and Newton's method for a nonlinear matrix equation, Linear and Multilinear Algebra, 2019, online (SCI).

[12].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).

[13].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).

[14].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).

[15].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).

[16].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).

[17].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).

[18].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).

[19].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).

[20].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).

[21].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).

[22].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).

[23].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).

[24].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).

[25].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).

[26].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).

[27].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).

[28].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).

[29].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).

[30].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 ).

[31].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).

[32].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).

[33].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).

[34].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).

[35].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).

[36].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).

[37].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).

[38].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).

[39].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).

[40].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).