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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
trzeros
transmission zeros and normal rank
Calling Sequence
[tr]=trzeros(Sl) [nt,dt,rk]=trzeros(Sl)
Arguments
- Sl
linear system (
syslin
list)- nt
complex vectors
- dt
real vector
- rk
integer (normal rank of Sl)
Description
Called with one output argument, trzeros(Sl)
returns the
transmission zeros of the linear system Sl
.
Sl
may have a polynomial (but square) D
matrix.
Called with 2 output arguments, trzeros
returns the
transmission zeros of the linear system Sl
as tr=nt./dt
;
(Note that some components of dt
may be zeros)
Called with 3 output arguments, rk
is the normal rank of Sl
Transfer matrices are converted to state-space.
If Sl
is a (square) polynomial matrix trzeros
returns the
roots of its determinant.
For usual state-space system trzeros
uses the state-space
algorithm of Emami-Naeni and Van Dooren.
If D
is invertible the transmission zeros are the eigenvalues
of the "A
matrix" of the inverse system : A - B*inv(D)*C
;
If C*B
is invertible the transmission zeros are the eigenvalues
of N*A*M
where M*N
is a full rank factorization of
eye(A)-B*inv(C*B)*C
;
For systems with a polynomial D
matrix zeros are
calculated as the roots of the determinant of the system matrix.
Caution: the computed zeros are not always reliable, in particular
in case of repeated zeros. |
Examples
W1=ssrand(2,2,5);trzeros(W1) //call trzeros roots(det(systmat(W1))) //roots of det(system matrix) s=poly(0,'s');W=[1/(s+1);1/(s-2)];W2=(s-3)*W*W';[nt,dt,rk]=trzeros(W2); St=systmat(tf2ss(W2));[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(St); St1=Q*St*Z;rowf=(Qd(1)+Qd(2)+1):(Qd(1)+Qd(2)+Qd(3)); colf=(Zd(1)+Zd(2)+1):(Zd(1)+Zd(2)+Zd(3)); roots(St1(rowf,colf)), nt./dt //By Kronecker form
See Also
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