trzeros - transmission zeros and normal rank
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 & 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.
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