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2 Frequency-domain condition for linear time-invariant systems Under this assumption, the following simple. 1. Time-domain condition for linear time-invariant systems Continuous-time necessary and sufficient conditionor a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, h ( t ). A necessary and sufficient condition for BIBO stability is derived which mainly relies on the asymptotic expansion of the impulse response f(t). A necessary and su cient condition for BIBO stability is: the closed loop transfer function P(s) C(sI A) 1 + D (1.2) has all poles in the open left-half of the complex plane (all poles have real part strictly smaller than 0). 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. x(t) B1, for all t, to determine if the system is BIBO stable, we need to determine if. 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. We can tell if an LTI system is BIBO stable from its impulse response. The approach is based on complex analysis. Stability Stability is the utmost important specification in control design After stability, we look at performance (tracking, disturbance and noise rejection, etc. 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. Applications: BIBO is generally used in areas where high-risk or high-isolation requirements exist, such as chemical and biological protection, radioactive protection, nuclear power stations, hospital isolation rooms, genetics and biotechnology labs.
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