# tzero

Invariant zeros of linear system.

## Syntax

* z = tzero(sys)
* z = tzero(A, B, C, D)
* z = tzero(A, B, C, D, E)
* \[z, nrank] = tzero(sys)
* \[z, nrank] = tzero(A, B, C, D)
* \[z, nrank] = tzero(A, B, C, D, E)

## Input argument

* sys - a LTI model.
* A - State matrix: Nx-by-Nx matrix.
* B - Input-to-state matrix: Nx-by-Nu matrix.
* C - State-to-output matrix: Ny-by-Nx matrix.
* D - Feedthrough matrix: Ny-by-Nu matrix.
* E - Nx-by-Nx matrix.

## Output argument

* Z - Invariant zeros: column vector.
* nrank - Normal rank: positive integer.

## Description

tzero function is employed to extract the invariant zeros of a Multiple Input, Multiple Output (MIMO) dynamic system described by the system model sys.

In cases where sys is a minimal realization, these invariant zeros coincide with the transmission zeros of the system.

## Example

```matlab
A = [1 2; 3 4];
B = [1; 0];
C = [1 0];
D = 0;
sys = ss(A, B, C, D);
z = tzero(sys)
[z, nrank] = tzero(sys)
```

## See also

[append](append).

## History

| Version | Description     |
| ------- | --------------- |
| 1.0.0   | initial version |

## Author

Allan CORNET
