Numerical solution of discrete-time algebraic Riccati equation

In this paper, we present a naturally numerical method for finding the maximal hermitian solution X+ of the Discrete-Time Algebraic Riccati Equation (DTARE) based on the convergence of a monotone sequence of hermitian matrices. MIRAMARE TRIESTE August 1999 E-mail: nktan@mathdep.hcmuns.edu.vn 227 Nguyen Van Cu, Q5, HCMC, Vietnam.

[1]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[2]  A. MacFarlane An Eigenvector Solution of the Optimal Linear Regulator Problem , 1963 .

[3]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[4]  J. Potter Matrix Quadratic Solutions , 1966 .

[5]  D. Kleinman On an iterative technique for Riccati equation computations , 1968 .

[6]  Axel Ruhe An algorithm for numerical determination of the structure of a general matrix , 1970 .

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

[8]  K. Mårtensson,et al.  On the matrix riccati equation , 1971, Inf. Sci..

[9]  K. Mrtensson On the matrix riccati equation , 1971 .

[10]  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.

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

[12]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[13]  A. Zinober Matrices: Methods and Applications , 1992 .

[14]  P. Lancaster,et al.  Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review , 1991 .

[15]  A modified Schur method for solving algebraic Riccati equations , 1991 .

[16]  A. Weeren,et al.  The discrete time Riccati equation related to the H∞ control problem , 1992, 1992 American Control Conference.

[17]  A. B. Rami Shani,et al.  Matrices: Methods and Applications , 1992 .

[18]  A. Weeren,et al.  The discrete-time Riccati equation related to the H∞ control problem , 1994, IEEE Trans. Autom. Control..

[19]  Alan J. Laub,et al.  Numerical improvements for solving Riccati equations , 1997, IEEE Trans. Autom. Control..