Mu Analysis and Synthesis Toolbox

Convert to and from CONSTANT and SYSTEM matrices

Syntax

• sys = pss2sys(mat,n) 
  sys = pck(A,B,C,D) 
  sys = pck(A,B,C) 
  [A,B,C,D] = unpck(sys) 
  mat = sys2pss(sys)
  

Description
pss2sys translates a regular MATLAB matrix that is in packed form into a SYSTEM matrix. mat contains [A B; C D] which describes the individual components of a SYSTEM matrix with n being the number of states (size of A). sys2pss returns the CONSTANT matrix, mat = [A B; C D], from the input SYSTEM matrix sys.

pck takes consistent state-space data and forms a SYSTEM matrix with the data structure defined. Consistent state-space data requires a square A matrix, a B matrix with the same number of rows as A, a C matrix with the same number of columns as A, and a D matrix with same number of columns of B and rows of C. If the fourth input argument is omitted, then the D matrix is assumed to be identically zero, of appropriate dimensions. unpck is the inverse operation of pck, taking a SYSTEM matrix sys and converting it to A, B, C and D CONSTANT matrices.

Note that based on the data structure definition, a -Inf in the bottom right corner of a matrix denotes a SYSTEM matrix, with the top, right corner element of the matrix containing the number of states.

Examples
Create a SYSTEM matrix from MATLAB CONSTANT matrices via pss2sys. Define matrices A, B, C, and D as follows:

• A = [-1 1; -1 -3]; B =[2 2; 2 2]i C = [3 3]; D = [4 4]
  mat = [A B; C D];
  sys = pss2sys(mat,2);
  minfo(mat)
  3 rows4 cols: regular MATLAB matrix
  mat =
      -1           1                22
      -1           -3               22
      3            3                44
  minfo(sys)
  system: 2 states1 outputs2 inputs
  seesys(sys)
  
  -1.0e+00     1.0e+00  |  2.0e+00     2.0e+00
  -1.0e+00    -3.0e+00  |  2.0e+00     2.0e+00
  ----------------------|----------------------
   3.0e+00     3.0e+00  |  4.0e+00     4.0e+00
  
  

• sys = pck(A,B,C,D);
  minfo(sys)
  system: 2 states1 outputs2 inputs
  seesys(sys)
  
  -1.0e+00     1.0e+00  |  2.0e+00     2.0e+00
  -1.0e+00    -3.0e+00  |  2.0e+00     2.0e+00
  ----------------------|----------------------
   3.0e+00     3.0e+00  |  4.0e+00     4.0e+00
  
  

Matrices A, B, C, and D can be constructed from sys using unpck.

• [A,B,C,D] = unpck(sys); 
  A
  A = 
      -1           1
      -1           3
  B
  B = 
      2            2
      2            2
  C
  C = 
      3            3
  D
  D = 
      4            4
  mat = sys2pss(sys); 
  mat
  mat =
      -1           1   2            2
      -1           -3  2            2
      3            3   4            4
  

See Also
minfo, nd2sys, vpck, vunpck, zp2sys

negangle

pkvnorm, vnorm