Compute poles of dynamic system
pole(sys) computes the
p of the SISO or MIMO dynamic system model
sys has internal delays, poles are obtained
by first setting all internal delays to zero (creating a zero-order
Padé approximation) so that the system has a finite number of
zeros. For some systems, setting delays to 0 creates singular algebraic
loops, which result in either improper or ill-defined, zero-delay
approximations. For these systems,
an error. This error does not imply a problem with the model
Multiple poles are numerically sensitive and cannot be computed to high accuracy. A pole λ with multiplicity m typically gives rise to a cluster of computed poles distributed on a circle with center λ and radius of order
where ε is the relative machine precision (
For state-space models, the poles are the eigenvalues of the A matrix, or the generalized eigenvalues of A – λE in the descriptor case.
For SISO transfer functions or zero-pole-gain models, the poles
are simply the denominator roots (see
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.