• Let G(s) be a p×m transfer matrix and let (A,B,C,D) be a minimal realization. Let the input
be u(t)=u0elt, where l is not a pole of G(s) and u0Î Cm is an arbitrary
constant vector, then the output with the initial state x(0)=(lI-A)-1Bu0 is y(t)=G(l)u0elt.
• Let G(s) be a p×m transfer matrix and let (A,B,C,D) be a minimal realization. Suppose that z0 is a
transmission zero of G(s) and is not a pole of G(s). Then for any nonzero vector u0Î Cm such that G(z0)u0=0, the output of the system
due to the initial state x(0)=(z0I-A)-1Bu0 and the input u(t)=u0ez0 t is identically zero: y(t)=G(z0) u0ez0 t=0.
• Computing Invariant Zeros: generalized
eigenvalue problem
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• MATLAB
command: eig(M,N).