  We consider the input/output-stability of linear time-invariant
single-input/single-output systems in terms of singularities of the transfer
function F(s) in Laplace domain. The approach is based on complex analysis. A
fairly general class of transfer functions F(s) is considered which can roughly
be characterized by two properties: (1) F(s) is meromorphic with a finite
number of poles in the open right half plane and (2), on the imaginary axes,
F(s) may have at most a finite number of poles and branch points. For this
class of systems, a complete and thorough characterization of BIBO stability in
terms of the singularities in the closed right half-plane is developed where no
necessity arises to differentiate between commensurate and incommensurate
orders of branch points as often done in literature. A necessary and sufficient
condition for BIBO stability is derived which mainly relies on the asymptotic
expansion of the impulse response f(t). The second main result is the
generalization of the well-known Nyquist citerion for testing closed-loop
stability in terms of the open-loop frequency response locus to the class of
systems under consideration which is gained by applying Cauchy's argument
principle.
