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Solved Problems-6

Problems-6
Determine whether the following continuous-time systems are stable:
  1. Description: Description: Description: 3050.png
  2. Description: Description: Description: 3046.png
Solution
Here, let the input be bounded.
  1. Description: Description: Description: 3042.png
As t → ∞, y(t) → ∞ [since x(t) is multiplied by t]
 
Hence, the system is an unstable system.
  1. Description: Description: Description: 3034.png
Here x(t) is multiplied by Description: Description: Description: 3029.png. We know that the value of sine varies between –1 and 1.
 
Hence y(t) is bounded as long as x(t) is bounded. Hence the system is stable.
 




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