Numerical solution of ATS + SA + Q = 0

A survey of techniques to solve ATS + SA + Q = 0 is presented, and nine algorithms are coded and tested on a batch of examples. Which algorithm to be recommended depends mainly on the order of the system.

[1]  R. A. Smith.  Matrix Equation $XA + BX = C$ , 1968 .

[2]  E. Davison,et al.  The numerical solution of A'Q+QA =-C , 1968 .

[3]  Antony Jameson,et al.  Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix , 1968 .

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

[5]  L. Shieh,et al.  A note on expanding PA + A^{T}P= -Q , 1968 .

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

[7]  C. Storey,et al.  The Liapunov matrix equation and Schwarz's form , 1967 .

[8]  Antony Jameson,et al.  Comparison of four numerical algorithms for solving the Liapunov matrix equation , 1970 .

[9]  C. Storey,et al.  Some Applications of the Lyapunov Matrix Equation , 1968 .

[10]  C. Storey,et al.  Remarks on numerical solution of the Lyapunov matrix equation , 1967 .

[11]  D. Faddeev,et al.  Computational Methods of Linear Algebra , 1959 .

[12]  P. Müller,et al.  Die Berechnung von Ljapunov-Funktionen und von quadratischen Regelflächen für lineare, stetige, zeitinvariante Mehrgrößensysteme , 1969 .

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

[14]  P. Parks.  A new proof of the Hurwitz stability criterion by the second method of Liapunov, with applications to "Optimum" transfer functions , 1963 .

[15]  D. Luenberger.  Observers for multivariable systems , 1966 .

[16]  C. Storey,et al.  Insensitivity of Optimal Linear Control Systems to Persistent Changes in Parameters , 1966 .

[17]  S. Bingulac.  An alternate approach to expanding PA+A'P=-Q , 1970 .

[18]  B. Anderson.  An algebraic solution to the spectral factorization problem , 1967, IEEE Transactions on Automatic Control.

[19]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[20]  R. A. Smith,et al.  Matrix calculations for Liapunov quadratic forms , 1966 .

[21]  B. P. Molinari,et al.  Algebraic solution of matrix linear equations in control theory , 1969 .

[22]  Er-Chieh Ma.  A Finite Series Solution of the Matrix Equation $AX - XB = C$ , 1966 .

[23]  Antony Jameson,et al.  SOLUTION OF EQUATION AX + XB = C BY INVERSION OF AN M × M OR N × N MATRIX ∗ , 1968 .

[24]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[25]  O. Taussky.  Matrices C with Cn → 0 , 1964 .