szeros (Mu Analysis and Synthesis Toolbox)

Mu Analysis and Synthesis Toolbox

szeros

Transmission zeros of a SYSTEM matrix

Syntax

```
veczeros = szeros(sys,epp)
```

Description
szeros calculates the transmission zeros of the input SYSTEM matrix, sys. The output veczeros contains the vector of transmission zeros.

epp is an optional input argument which is used to test the closeness of the generalized eigenvalues of the randomly perturbed matrices. Its default value is the machine epsilon. Occasionally zeros at infinity are displayed as very large values due to numerical accuracy problems.

For a square SYSTEM matrix, [A B; C D], the generalized eigenvalue test consists of finding the roots of:

Algorithm
For a square system, the transmission zeros are found via the generalized eigenvalue problem described above. To solve for the transmission zeros of a nonsquare SYSTEM matrix, additional random rows or columns are augmented to the SYSTEM matrix to make it square and the corresponding zeros are found. This is done twice, and the unchanged generalized eigenvalues, where the difference between the eigenvalues is less than epp, are considered to be the transmission zeros of the SYSTEM matrix.

Reference
Laub, A.J., and B.C. Moore, "Calculation of transmission zeros using QZ techniques," Automatica, vol. 14, pp. 557-563, 1978.

See Also
spoles

sysic trsp, dtrsp, sdtrsp