![]() ![]() A necessary (but not sufficient) condition for stability is. Since (S) is BIBO stable, for ech u with u < a,for each (Xo. If an < 0, we multiply Equation 6 by -1 to generate a new equation that satisfies this condition. Because of the conditions (2), (3) imposed on f, x(r) is defined. The region of convergence must therefore include the unit circle. Theorem 4.2 establishes necessary and sufficient conditions for BIBO stability of a discrete-time linear system. The Routh Stability Criterion is based on a characteristic equation that has the form 1 0 1 + 1 + + + o n n n ans a s L a s a (6) We arbitrarily assume that an > 0. Time-domain condition for linear time-invariant systems Continuous-time necessary and sufficient condition įor a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, h ( t ). 2 Frequency-domain condition for linear time-invariant systems.1.1 Continuous-time necessary and sufficient condition.1 Time-domain condition for linear time-invariant systems. ![]()
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