Upper matrix bound of the solution for the discrete Riccati equation

A new upper matrix bound of the solution for the discrete algebraic matrix Riccati equation is developed. This matrix bound is then used to derive bounds on the eigenvalues, trace, and determinant of the same solution. It is shown that these eigenvalue bounds are less restrictive than previous results.

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

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

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

[4]  Chien-Hua Lee.  Simple stabilizability criteria and memoryless state feedback control design for time-delay systems with time-varying perturbations , 1998 .

[5]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[6]  W. Rugh.  Linear System Theory , 1992 .

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

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

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

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

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

[12]  N. Komaroff,et al.  Iterative matrix bounds and computational solutions to the discrete algebraic Riccati equation , 1994, IEEE Trans. Autom. Control..

[13]  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 .

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

[15]  M. T. Tran,et al.  A note on the discrete Lyapunov and Riccati matrix equations , 1984 .

[16]  H. Weyl.  Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

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