Description: The stability of the Z-transform is a fundamental property that determines the behavior of a system in the Z domain, which is used in the analysis and design of discrete systems. This property refers to a system’s ability to return to an equilibrium state after a disturbance. In technical terms, a system is considered stable if all the roots of its transfer function, obtained from the Z-transform, lie within the unit circle in the Z-plane. This implies that the system’s responses to bounded inputs do not diverge, which is crucial for ensuring predictable and controllable performance. Stability is a critical aspect in control system design, as an unstable system can lead to undesirable behaviors, such as oscillations or divergences in output. Therefore, evaluating stability through the Z-transform is essential in applications ranging from signal processing to control systems, where the goal is to ensure that the system operates efficiently and safely. In summary, the stability of the Z-transform is a key concept that allows engineers and scientists to evaluate and design discrete systems that are robust and reliable.
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