Which of the following is a characteristic of a stable system?

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Question: Which of the following is a characteristic of a stable system?

Options:

Correct Answer: All poles are in the left half of the s-plane.

Solution:

A stable system has all its poles located in the left half of the s-plane, ensuring that the system response decays over time.

Which of the following is a characteristic of a stable system?

Which of the following is a characteristic of a stable system?

Step 1: Understand what a system is. A system can be anything that takes input and produces output, like a machine or a control system.
Step 2: Learn about stability. A stable system is one that behaves predictably over time, meaning it doesn't go out of control.
Step 3: Know about poles. In control systems, poles are specific values that help determine how the system behaves. They are found in a mathematical representation called the s-plane.
Step 4: Identify the left half of the s-plane. The s-plane is a graph where the horizontal axis represents real numbers. The left half is where the real numbers are negative.
Step 5: Understand the significance of poles in the left half. If all the poles of a system are in the left half of the s-plane, it means the system will return to a steady state over time, leading to a stable response.
Step 6: Conclude that a characteristic of a stable system is that all its poles are located in the left half of the s-plane.

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