Which of the following indicates that a system is stable?

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Question: Which of the following indicates that a system is stable?

Options:

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

Solution:

A system is stable if all poles of its transfer function are located in the left half of the s-plane.

Which of the following indicates that a system is stable?

Which of the following indicates that a system is stable?

Step 1: Understand what a system is in control theory. A system can be anything that takes input and produces output, like a car or a robot.
Step 2: Learn about the transfer function. The transfer function is a mathematical representation that describes how the output of a system responds to its input.
Step 3: Know what poles are. Poles are specific values in the transfer function that help determine the behavior of the system.
Step 4: Identify the s-plane. The s-plane is a graph where the horizontal axis represents the real part of the poles and the vertical axis represents the imaginary part.
Step 5: Understand the left half of the s-plane. The left half of the s-plane is where the real part of the poles is negative.
Step 6: Determine stability. A system is stable if all its poles are located in the left half of the s-plane, meaning they all have negative real parts.

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