Invariant zeros of linear system
z = tzero(sys)
z = tzero(A,B,C,D,E)
z = tzero(___,tol)
[z,nrank]
= tzero(___)
returns
the invariant zeros of
the multiinput, multioutput (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 statespace model z
= tzero(A,B,C,D,E
)
$$\begin{array}{c}E\frac{dx}{dt}=Ax+Bu\\ y=Cx+Du.\end{array}$$
Omit E
for an explicit statespace model
(E = I).
specifies
the relative tolerance, z
= tzero(___,tol
)tol
, controlling rank
decisions.
[
also returns the normal rank of
the transfer function of z
,nrank
]
= tzero(___)sys
or of the transfer
function H(s) = D + C(sE – A)^{–1}B.

MIMO dynamic
system model. If 

Statespace matrices describing the linear system $$\begin{array}{c}E\frac{dx}{dt}=Ax+Bu\\ y=Cx+Du.\end{array}$$
Omit 

Relative tolerance controlling rank decisions. Increasing tolerance helps detect nonminimal modes and eliminate very large zeros (near infinity). However, increased tolerance might artificially inflate the number of transmission zeros. Default: 

Column vector containing the invariant zeros of 

Normal rank of the transfer function of To obtain a meaningful result for 
You can use the syntax z = tzero(A,B,C,D,E)
to
find the uncontrollable or unobservable modes of a statespace model.
When C
and D
are empty or zero, tzero
returns
the uncontrollable modes of (AsE,B)
. Similarly,
when B
and D
are empty or zero, tzero
returns
the unobservable modes of (C,AsE)
. See Identify Unobservable and Uncontrollable Modes of MIMO Model for an
example.
tzero
is based on SLICOT routines AB08ND, AB08NZ, AG08BD, and AG08BZ.
tzero
implements the algorithms in [1] and [2].
To calculate the zeros and gain of a singleinput, singleoutput
(SISO) system, use zero
.
[1] EmamiNaeini, 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 StateSpace Systems,” Automatica, 30 (1994), pp. 19211936.