System #1 is described by y(t) = ramp (x(t)) and system #2 is described by y(t) = x(t) ramp(t). Classify both systems as to BIBO stability, linearity, invertibility and time invariance.

Question

What will be an ideal response?

Answer 1

SOLUTION:

System #1:



If the excitation is bounded, the response is also bounded. Therefore the system is BIBO stable.



For any negative value of excitation the response is zero. Therefore when the response is zero it is impossible to determine the excitation. Therefore the system is not invertible.



System #2:



The ramp function is unbounded as time approaches positive infinity. Therefore, even if the excitation is bounded the response is unbounded. Therefore the system is not BIBO stable.



For any negative value of time the response is zero. Therefore when the response is zero it is impossible to determine the excitation. Therefore the system is not invertible.