System Stability in Signals and Systems
In the context of signals and systems, system stability refers to the ability of a system to return to a state of equilibrium after experiencing a disturbance. A stable system will exhibit bounded output for a bounded input, meaning that the output remains within certain limits over time. In practical terms, this means that the system is able to maintain a steady response to input signals without diverging or oscillating uncontrollably.
There are various criteria used to determine system stability, such as the bounded-input, bounded-output (BIBO) stability criterion, the Routh-Hurwitz stability criterion, and the Nyquist stability criterion. These criteria help analyze the behavior of a system under different conditions and ensure that the system is robust and reliable in its response to input signals.
Understanding system stability is crucial in the design and analysis of signal processing systems, control systems, communications systems, and other applications of signals and systems. By ensuring that a system is stable, engineers can predict and control its behavior, leading to improved performance and reliability.
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