A necessary and sufficient condition for BIBO stability is derived which mainly relies on the asymptotic expansion of the impulse response f(t). 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 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. The approach is based on complex analysis. 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.
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