The improved upper solution bounds of the continuous coupled algebraic Riccati matrix equation

详细信息    查看全文

• 作者：Juan Zhang (1) (2) (3)
  Jianzhou Liu (1) (2) (3)
  
• 关键词：Continuous coupled algebraic Riccati equation ; eigenvalue ; matrix bound
• 刊名：International Journal of Control, Automation and Systems
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：11
• 期：4
• 页码：852-858
• 全文大小：1234KB
• 参考文献：1. A. Czornik and A. Swierniak, “Lower bounds on the solution of coupled algebraic Riccati equation,- / Automatica, vol. 37, no. 4, pp. 619-24, 2001. 10.1016/S0005-1098(00)00196-5">CrossRef
  2. M. A. Rami and L. El Ghaoui, “LMI optimization for nonstandard Riccati equations arising in stochastic control,- / IEEE Trans. on Automatic Control, vol. 41, no. 11, pp. 1666-671, 1996. 10.1109/9.544005">CrossRef
  3. Y. Ji and H. J. Chizeck, “Controllability, observability and continuous-time Markovian jump linear quadratic control,- / IEEE Trans. on Automatic Control, vol. 35, no. 7, pp. 777-88, 1990. 10.1109/9.57016">CrossRef
  4. Y. Fang and K. A. Loparo, “Stabilization of continuous-time jump linear systems,- / IEEE Trans. on Automatic Control, vol. 47, no. 10, pp. 1590-603, 2002. 10.1109/TAC.2002.803528">CrossRef
  5. C.-H. Lee, “New upper solution bounds of the continuous algebraic Riccati matrix equation,- / IEEE Trans. on Automatic Control, vol. 51, no. 2, pp. 330-34, 2006. 10.1109/TAC.2005.863514">CrossRef
  6. R. Davies, P. Shi, and R. Wiltshire, “New lower solution bounds of the continuous algebraic Riccati matrix equation,- / Linear Algebra and its Applications, vol. 427, no. 2-, pp. 242-55, 2007. 10.1016/j.laa.2007.07.017">CrossRef
  7. J. Zhang and J.-Z. Liu, “New lower solution bounds for the continuous algebraic Riccati equation,- / Electronic Journal of Linear Algebra, vol. 22, pp. 191-02, 2011.
  8. J. Zhang and J.-Z. 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.
  9. J.-Z. Liu, J. Zhang, and Y. Liu, “New solution bounds for the continuous algebraic Riccati equation,- / Journal of the Franklin Institute, vol. 348, no. 8, pp. 2128-141, 2011. 10.1016/j.jfranklin.2011.06.007">CrossRef
  10. A. Czornik and A. Swierniak, “Upper bounds on the solution of coupled algebraic Riccati equation,- / Journal of Inequalities and Applications, vol. 6, pp. 373-85, 2001.
  11. C.-H. Lee, “An improved lower matrix bound of the solution of the unified coupled Riccati equation,- / IEEE Trans. on Automatic Control, vol. 50, no. 8, pp. 1221-223, 2005. 10.1109/TAC.2005.852560">CrossRef
  12. L. Gao, A. Xue, and Y. Sun, “Matrix bounds for the coupled algebraic Riccati equation,- / Proc. of the 4th World Congress on Intelligent Control and Automation, pp. 180-83, 2002.
  13. R. Davies, P. Shi, and R. Wiltshire, “Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations,- / Automatica, vol. 44, no. 4, pp. 1088-096, 2008. 10.1016/j.automatica.2007.11.001">CrossRef
  14. J.-Z. Liu and J. Zhang, “Upper solution bounds of the continuous coupled algebraic Riccati matrix equation,- / International Journal of Control, vol. 84, no. 4, pp. 726-36, 2011. 10.1080/00207179.2011.573001">CrossRef
  15. A. W. Marshall and I. Olkin, / Inequalities Theory of Majorsation and Its Applications, Academic Press, New York, 1979.
  16. D. S. Bernstein, / Matrix Mathematics: Theory, Facts and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ, 2005.
  17. A. Berman and R. J. Plemmons, / Nonnegative Matrices in the Mathematical Science, Academic Press, New York, 1979.
  
• 作者单位：Juan Zhang (1) (2) (3)
  Jianzhou Liu (1) (2) (3)
  
  1. Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P. R. China
  2. Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan, 411105, China
  3. Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, Hunan, 411105, China
  

文摘

In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then, in terms of the properties of M-matrix and its inverse matrix, through solving the derived linear inequalities, we offer new upper matrix bounds for the solution of the CCARE, which improve some of the recent results. Finally, we present a corresponding numerical example to show the effectiveness of the given results.