Perturbation Theory for Algebraic Riccati Equations

New perturbation results for the two different algebraic Riccati equations (continuous time and discrete time) are derived in a uniform manner. The new results are illustrated by numerical examples.

[1]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[2]  G. Stewart.  Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .

[3]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[4]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[5]  P. Dooren.  A Generalized Eigenvalue Approach for Solving Riccati Equations , 1980 .

[6]  A. Laub,et al.  On the numerical solution of the discrete-time algebraic Riccati equation , 1980 .

[7]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[8]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  A. Laub,et al.  Generalized eigenproblem algorithms and software for algebraic Riccati equations , 1984, Proceedings of the IEEE.

[11]  C. Loan.  How Near is a Stable Matrix to an Unstable Matrix , 1984 .

[12]  Stephen G. Nash,et al.  On the singular “Vectors of the Lyapunov operator , 1987 .

[13]  Volker Mehrmann,et al.  A symplectic orthogonal method for single input or single ouput discrete time optimal quadratic control problems , 1988 .

[14]  Petko Hr. Petkov,et al.  Perturbation Analysis of Matrix Quadratic Equations , 1990, SIAM J. Sci. Comput..

[15]  Alan J. Laub,et al.  Error bounds for Newton refinement of solutions to algebraic riccati equations , 1990, Math. Control. Signals Syst..

[16]  Alan J. Laub,et al.  Sensitivity of the stable discrete-time Lyapunov equation , 1990 .

[17]  G. Hewer,et al.  The sensitivity of the algebraic and differential riccati equations , 1990 .

[18]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[19]  Vlad Ionescu,et al.  On computing the stabilizing solution of the discrete-time Riccati equation , 1992 .

[20]  Alan J. Laub,et al.  Scaling of the discrete-time algebraic Riccati equation to enhance stability of the Schur solution method , 1992 .

[21]  Petko Hr. Petkov,et al.  Perturbation analysis of the discrete Riccati equation , 1993, Kybernetika.

[22]  R. D. Murphy,et al.  Iterative solution of nonlinear equations , 1994 .

[23]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[24]  Shu-Fang Xu,et al.  Sensitivity analysis of the algebraic Riccati equations , 1996 .

[25]  Ji-guang Sun,et al.  Residual bounds of approximate solutions of the algebraic Riccati equation , 1997 .

[26]  Ji-guang Sun,et al.  Backward error for the discrete-time algebraic riccati equation , 1997 .

[27]  Ji-guang Sun,et al.  Residual bounds of approximate solutions of the discrete-time algebraic Riccati equation , 1998 .