# tzero

Invariant zeros of linear system

## Description

returns
the invariant zeros of MIMO dynamic
system, `z`

= tzero(`sys`

)`sys`

. If `sys`

is a minimal realization, the
invariant zeros coincide with the transmission zeros of
`sys`

.

returns the invariant
zeros of the state-space model described by matrices `z`

= tzero(`A,B,C,D,E`

)*A*,
*B*, *C*, *D*, and
*E*.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

You can use the syntax

`z = tzero(A,B,C,D,E)`

to find the uncontrollable or unobservable modes of a state-space model. When`C`

and`D`

are empty or zero,`tzero`

returns the uncontrollable modes of`(A-sE,B)`

. Similarly, when`B`

and`D`

are empty or zero,`tzero`

returns the unobservable modes of`(C,A-sE)`

. For an example, see Identify Unobservable and Uncontrollable Modes of MIMO Model.

## Algorithms

`tzero`

is based on SLICOT routines AB08ND, AB08NZ, AG08BD, and AG08BZ.
`tzero`

implements the algorithms in [1] and [2].

## References

[1] Emami-Naeini, A. and P. Van
Dooren, "Computation of Zeros of Linear Multivariable Systems,"
*Automatica*, 18 (1982), pp. 415–430.

[2] Misra, P, P. Van Dooren, and A.
Varga, "Computation of Structural Invariants of Generalized State-Space Systems,"
*Automatica*, 30 (1994), pp. 1921-1936.

## Version History

**Introduced in R2012a**