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Solution Bounds of the Continuous and Discrete Lyapunov Matrix Equations

Author

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  • C. H. Lee

    (Cheng-Shiu University)

Abstract

A unified approach is proposed to solve the estimation problem for the solution of continuous and discrete Lyapunov equations. Upper and lower matrix bounds and corresponding eigenvalue bounds of the solution of the so-called unified algebraic Lyapunov equation are presented in this paper. From the obtained results, the bounds for the solutions of continuous and discrete Lyapunov equations can be obtained as limiting cases. It is shown that the eigenvalue bounds of the unified Lyapunov equation are tighter than some parallel results and that the lower matrix bounds of the continuous Lyapunov equation are more general than the majority of those which have appeared in the literature.

Suggested Citation

  • C. H. Lee, 2004. "Solution Bounds of the Continuous and Discrete Lyapunov Matrix Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 559-578, March.
    • Handle: RePEc:spr:joptap:v:120:y:2004:i:3:d:10.1023_b:jota.0000025710.59589.80
    DOI: 10.1023/B:JOTA.0000025710.59589.80
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    Cited by:

    1. Juan Zhang & Shifeng Li & Xiangyang Gan, 2022. "Solution Bounds and Numerical Methods of the Unified Algebraic Lyapunov Equation," Mathematics, MDPI, vol. 10(16), pages 1-19, August.

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