New lower matrix bounds for the solution of the continuous algebraic lyapunov equation

New lower matrix bounds are derived for the solution of the continuous algebraic Lyapunov equation (CALE). Following each bound derivation, an iterative algorithm is proposed to derive tighter matrix bounds. In comparison to existing results, the presented results are more concise and are always valid when the CALE has a non-negative definite solution. We finally give numerical examples to show the effectiveness of the derived bounds and make comparisons with existing results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

[1]  C. H. Lee.  Further results on the measurement of solution bounds of the generalized Lyapunov equations , 2003, J. Frankl. Inst..

[2]  C. H. Lee.  Solution Bounds of the Continuous and Discrete Lyapunov Matrix Equations , 2004 .

[3]  T. Mori,et al.  Explicit solution and eigenvalue bounds in the Lyapunov matrix equation , 1986 .

[4]  F. Kung,et al.  Upper and lower matrix bounds of the solutions for the continuous and discrete Lyapunov equations , 1997 .

[5]  Chien-Hua Lee,et al.  New results for the bounds of the solution for the continuous Riccati and Lyapunov equations , 1997, IEEE Trans. Autom. Control..

[6]  Chien-Hua Lee,et al.  On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems , 2001 .

[7]  Han Ho Choi,et al.  Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations , 2002, Autom..

[8]  Chien-Hua Lee,et al.  On the upper and lower bounds of the solution for the continuous Riccati matrix equation , 1997 .

[9]  Tzuu-Hseng S. Li,et al.  A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays , 1993 .

[10]  M. Basin,et al.  OPTIMAL STATE ESTIMATION FOR CONTINUOUS STOCHASTIC STATE-SPACE SYSTEM WITH HYBRID MEASUREMENTS , 2006 .

[11]  On bounds of Lyapunov's matrix equation , 1979 .

[12]  Svetoslav G. Savov,et al.  New upper estimates for the solution of the continuous algebraic Lyapunov equation , 2004, IEEE Transactions on Automatic Control.

[13]  Bor-Sen Chen,et al.  Robust stability of uncertain time-delay systems , 1987 .

[14]  Wook Hyun Kwon,et al.  A note on the algebraic matrix Riccati equation , 1977 .

[15]  Young Soo Moon,et al.  Bounds in algebraic Riccati and Lyapunov equations: a survey and some new results , 1996 .

[16]  Chien-Hua Lee.  Solution bounds of the continuous Riccati matrix equation , 2003, IEEE Trans. Autom. Control..

[17]  Yuguang Fang,et al.  New estimates for solutions of Lyapunov equations , 1997, IEEE Trans. Autom. Control..

[18]  I. Troch.  Improved bounds for the eigenvalues of solutions of Lyapunov equations , 1987 .

[19]  Youxian Sun,et al.  Comments on "Upper matrix bounds for the discrete algebraic Riccati matrix equation" [with author's reply] , 2002, IEEE Trans. Autom. Control..