slicot_sb01bd

Pole assignment for a given matrix pair (A,B).

Syntax

• [A_OUT, WR_OUT, WI_OUT, NFP, NAP, NUP, F, Z, IWARN, INFO] = slicot_sb01bd(DICO, ALPHA, A_IN, B_IN, WR_IN, WI_IN, TOL)

Input argument

• DICO - Specifies the type of the original system.'C': continuous-time system;'D': discrete-time system.

• ALPHA - Specifies the maximum admissible value.

• A_IN - the leading N-by-N part of this array must contain the state dynamics matrix A.

• B_IN - The leading N-by-M part of this array must contain the input/state matrix.

• WR_IN - contains the real parts of the desired eigenvalues of the closed-loop system state-matrix A+B*F.

• WI_IN - contains the imaginary parts of the desired eigenvalues of the closed-loop system state-matrix A+B*F.

• TOL - The absolute tolerance level below which the elements of A or B are considered zero (used for controllability tests).

Output argument

• A_OUT - the leading N-by-N part of this array contains the matrix Z'(A+BF)*Z in a real Schur form.

• WR_OUT - if INFO = 0, the leading NAP elements of these arrays contain the real parts of the assigned eigenvalues. The trailing NP-NAP elements contain the unassigned eigenvalues.

• WI_OUT - if INFO = 0, the leading NAP elements of these arrays contain the imaginary parts of the assigned eigenvalues. The trailing NP-NAP elements contain the unassigned eigenvalues.

• NFP - The number of eigenvalues of A having real parts less than ALPHA, if DICO = 'C', or moduli less than ALPHA, if DICO = 'D'. These eigenvalues are not modified by the eigenvalue assignment algorithm.

• NAP - The number of assigned eigenvalues. If INFO = 0 on exit, then NAP = N-NFP-NUP.

• NUP - The number of uncontrollable eigenvalues detected by the eigenvalue assignment algorithm.

• F - The leading M-by-N part of this array contains the state feedback F, which assigns NAP closed-loop eigenvalues and keeps unaltered N-NAP open-loop eigenvalues.

• Z - The leading N-by-N part of this array contains the orthogonal matrix Z which reduces the closed-loop system state matrix A + B*F to upper real Schur form.

• IWARN - = 0: no warning; = K: K violations of the numerical stability condition.

• INFO - = 0: successful exit;

Description

To determine the state feedback matrix F for a given system (A,B) such that the closed-loop state matrix A+B*F has specified eigenvalues.

Used function(s)

SB01BD

Bibliography

http://slicot.org/objects/software/shared/doc/SB01BD.html

Example

N = 4;
M = 2;
NP = 2;
ALPHA = -.4;
TOL = 1.E-8;
DICO = 'C';

A_IN = [  -6.8000   0.0000  -207.0000   0.0000;
   1.0000   0.0000     0.0000   0.0000;
  43.2000   0.0000     0.0000  -4.2000;
   0.0000   0.0000     1.0000   0.0000];

B_IN = [   5.6400   0.0000;
   0.0000   0.0000;
   0.0000   1.1800;
   0.0000   0.0000];

WR_IN = [-0.5000; -0.5000];
WI_IN = [ 0.1500; -0.1500];

[A_OUT, WR_OUT, WI_OUT, NFP, NAP, NUP, F, Z, IWARN, INFO] = slicot_sb01bd(DICO, ALPHA, A_IN, B_IN, WR_IN, WI_IN, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation