Matrix solution bounds of the continuous Lyapunov equation by using a bilinear transformation

By using a bilinear transformation and some linear algebraic techniques, new matrix bounds of the solution of the continuous algebraic Lyapunov equation (CALE) are derived in this paper. Comparing to existing works, these obtained matrix bounds are less restrictive and are easy to be calculated. A numerical example is also given to demonstrate the merits of the present results.

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

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

[3]  E. Shapiro.  On the Lyapunov matrix equation , 1974 .

[4]  Chien-Hua Lee.  Eigenvalue upper and lower bounds of the solution for the continuous algebraic matrix Riccati equation , 1996 .

[5]  N. Komaroff.  Lower bounds for the solution of the discrete algebraic Lyapunov equation , 1992 .

[6]  A. R. Amir-Moéz.  Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations , 1956 .

[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]  N. Komaroff,et al.  Lower summation bounds for the discrete Riccati and Lyapunov equations , 1992 .

[10]  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..

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

[12]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

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

[14]  A. Hmamed,et al.  Discrete Lyapunov equation: simultaneous eigenvalue lower bounds , 1991 .

[15]  Te-son Kuo,et al.  Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation , 1986 .

[16]  T. Mori,et al.  A brief summary of the bounds on the solution of the algebraic matrix equations in control theory , 1984 .

[17]  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 .

[18]  Richard Davies,et al.  New lower matrix bounds for the solution of the continuous algebraic lyapunov equation , 2008 .

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

[20]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

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

[22]  M. T. Qureshi,et al.  Lyapunov Matrix Equation in System Stability and Control , 2008 .

[23]  Yannis A. Phillis,et al.  Trace bounds on the covariances of continuous-time systems with multiplicative noise , 1993, IEEE Trans. Autom. Control..

[24]  Rama K. Yedavalli,et al.  Robust root clustering for linear uncertain systems using generalized lyapunov theory , 1993, Autom..

[25]  J. Garloff.  Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equations and the continuous Lyapunov equation , 1986 .

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