The impulse response of a system is h(n)=α^nu(n). The condition for the system to be stable is
Answers
Answer:
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Concept:
The stability can be checked by using the final value theorem. If the variable is tending to be infinite and the value of the function comes outs to be finite, the system is said to be stable.
Given:
The impulse response of a system is h(n)=αⁿ u(n).
Find:
The condition for the system to be stable.
Solution:
If the output of the system is under control, a system is said to be stable. If it becomes out of control, it is said to be unstable. If the system is stable, it produces a bounded output for a given bounded input.
In the given function, the system is unbounded and the system gives infinite when the variable is infinite.
Hence, the condition for the system to be stable is a bounded output for a given bounded input.
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