Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations

In this paper, we propose lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations. We give comparisons between the parallel estimates. Finally, we give examples showing that our bounds can be better than the previous results for some cases.

[1]  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..

[2]  Rajnikant V. Patel,et al.  Bounds on performance of nonstationary continuous-time filters under modelling uncertainty , 1984, Autom..

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

[4]  M. Toda,et al.  On norm bounds for algebraic Riccati and Lyapunov equations , 1978 .

[5]  K. Hirai,et al.  Upper and lower bounds on the solution of the algebraic Riccati equation , 1979 .

[6]  C. Storey,et al.  Matrix methods in stability theory , 1972, The Mathematical Gazette.

[7]  V. Karanam A note on eigenvalue bounds in algebraic Riccati equation , 1983 .

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

[9]  Myung-Joong Youn,et al.  On bounds of the Riccati and Lyapunov matrix equations , 1985 .

[10]  A. Jameson,et al.  Conditions for nonnegativeness of partitioned matrices , 1972 .

[11]  Han Ho Choi Upper matrix bounds for the discrete algebraic Riccati matrix equation , 2001, IEEE Trans. Autom. Control..

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

[13]  T. Mori,et al.  Bounds in the Lyapunov matrix differential equation , 1987 .

[14]  Jin-Hoon Kim,et al.  Some bounds of the solution of the algebraic Riccati equation , 1992 .

[15]  Baxter F. Womack,et al.  Comments on "On the Lyapunov matrix equation" , 1975 .

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

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

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