Spectral norm and trace bounds of algebraic matrix Riccati equations

Upper bounds on spectral norm and trace for the solution of continuous algebraic matrix Riccati equations are proposed. The proposed bounds are based on a form of the general analytic solution. It is shown that, in many cases, the spectral norm and the trace bounds are better than other results.

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

[2]  J. Allwright,et al.  A lower bound for the solution of the algebraic Riccati equation of optimal control and a geometric convergence rate for the Kleinman algorithm , 1980 .

[3]  I. Rhodes,et al.  A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations , 1987 .

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

[5]  Takehiro Mori.  Comments on "A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equation" by J.M. Saniuk and I.B. Rhodes , 1988 .

[6]  V. Karanam.  Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations , 1981 .

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

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

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

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

[11]  N. Komaroff,et al.  Bounds on eigenvalues of matrix products with an application to the algebraic Riccati equation , 1990 .

[12]  M. Toda,et al.  Bounds on estimation errors of discrete-time filters under modeling uncertainty , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[13]  Mitsuhiko Toda,et al.  Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors , 1978, IEEE Transactions on Aerospace and Electronic Systems.

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

[15]  Comments on "On some bounds in the algebraic Riccati and Lyapunov equations" , 1986 .

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

[17]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

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

[20]  T. Mori,et al.  On the discrete Riccati equation , 1987 .

[21]  G. Langholz.  A new lower bound on the cost of optimal regulators , 1979 .

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

[23]  T. Mori.  On some bounds in the algebraic Riccati and Lyanupov equations , 1985, IEEE Transactions on Automatic Control.