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

  • Control Theory
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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P. R. China

    Juan Zhang & Jianzhou Liu

  2. Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan, 411105, China

    Juan Zhang & Jianzhou Liu

  3. Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, Hunan, 411105, China

    Juan Zhang & Jianzhou Liu

Authors
  1. Juan Zhang
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  2. Jianzhou Liu
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Correspondence to Juan Zhang.

Additional information

Recommended by Editorial Board member Shengyuan Xu under the direction of Editor Zengqi Sun.

This work was supported in part by Natural Science Foundation of China (10971176), the Key Project of Hunan Provincial Natural Science Foundation of China (10JJ2002), the Key Project of Hunan Provincial Education Department of China (12A137), Program for Changjiang Scholars and Innovative Research Team in University of China (No. IRT1179), the Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province of China.

Juan Zhang received her M.S. degree from the Department of Mathematics and Computational Science at Xiangtan University in 2009. Her research interests include control theory and its application, matrix analysis and its application.

Jianzhou Liu received his Ph.D. degree from the Department of Mathematics and Computational Science at Xiangtan University in 2003. His research interests include control theory and its application, numerical algebra, matrix analysis and its application.

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Zhang, J., Liu, J. The improved upper solution bounds of the continuous coupled algebraic Riccati matrix equation. Int. J. Control Autom. Syst. 11, 852–858 (2013). https://doi.org/10.1007/s12555-012-0188-9

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  • DOI: https://doi.org/10.1007/s12555-012-0188-9

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