I appreciate it if anybody could answer my question. Is the following comment correct?
"If a unit step signal is applied to an integrator, i.e. the simple system 1/s, the output will be unbounded. So there is a bounded input that gives an unbounded output. Therefore integrator is an unstable system."
Dear An. Thanks a lot for your answer. I am glad to find an answer for this question after three years. However, I am not convinced yet completely. The reference you cited says that we cannot conclude that a system is not stable because there are a bounded input that produces an unbounded output. Thus, the question is that what is the criterion based on it we can say a system is stable (why the simple integrator is stable)? Does the reference is differentiating the Lyapunov stability from BIBO stability? Thanks again for your interesting answer.
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