Specifications

pole
16-172
16pole
Purpose Compute the poles of an LTI system
Syntax p = pole(sys)
Description pole computes the poles p of the SISO or MIMO LTI model sys.
Algorithm For state-space models, the poles are the eigenvalues of the matrix, or the
generalized eigenvalues of in the descriptor case.
For SISO transfer functions or zero-pole-gain models, the poles are simply the
denominator roots (see
roots).
For MIMO transfer functions (or zero-pole-gain models), the poles are
computed as the union of the poles for each SISO entry. If some columns or
rows have a common denominator, the roots of this denominator are counted
only once.
Limitations Multiple poles are numerically sensitive and cannot be computed to high
accuracy. A pole with multiplicity typically gives rise to a cluster of
computed poles distributed on a circle with center and radius of order
where is the relative machine precision (
eps).
See Also damp Damping and natural frequency of system poles
esort, dsort Sort system poles
pzmap Pole-zero map
zero Compute (transmission) zeros
A
A
λ
E–
λ
m
λ
ρε
1 m
⁄
≈
ε