statecc, strans (Mu Analysis and Synthesis Toolbox)

Apply state-coordinate transformation to a SYSTEM matrix

Syntax

sysout = statecc(sysin,t) 
[sysout,v] = strans(sys)

Description

statecc applies a state coordinate transformation to the matrix, yielding a new SYSTEM matrix with

sysout = pck(tA*t,tB,C*t,D)

where A, B, C, and D are the state-space entries of the matrix sysin. t is restricted to be square and have the same dimensions as the A matrix.

strans transforms the A matrix of sys in bidiagonal form with the complex conjugate roots in real 2 x 2 form. sysout contains the transformed SYSTEM matrix and v is the transformation matrix. The A matrix is ordered by increasing magnitude of its eigenvalues. strans calls the MATLAB eig command to do the reordering.

Note:
strans may be inaccurate when a SYSTEM/CONSTANT matrix has repeated eigenvalues. This is due to the potential defective eigensystem, and the lack of a full set of eigenvectors.

Examples

The strans command shows the individual contributions of the modes of the SYSTEM matrix. In this example sys, which has four states, two inputs and one output is transformed into bidiagonal form.

see(sys)
A matrix
0.2190   0.9347   0.0346   0.0077
0.0470   0.3835   0.0535   0.3834
0.6789   0.5194   0.5297   0.0668
0.6793   0.8310   0.6711   0.4175

B matrix
0.6868   0.5269
0.5890   0.0920
0.9304   0.6539
0.8462   0.4160

C matrix
0.7012      0.9103    0.7622    0.2625

D matrix
O       O

sys=strc
see(sys)

A matrix
-0.0763         0          0         0
      0    0.1082    -0.4681         0
      0         0          0    1.4095

B matrix
-0.4731    -0.1839
 0.5971     0.3199
 0.2869     0.5542
-1.7033    -0.8132
C matrix
-0.1150     0.0298    0.3214     -1.0477 

D matrix
O       O