The discussion focuses on determining the Bounded Input Bounded Output (BIBO) stability of the linear time-invariant (LTI) system represented by the transfer function \( H(s) = \frac{s - 2}{(s + 2)(s + 1)(s - 1)} \). It is established that for a system to be BIBO stable, all poles of the transfer function must have negative real parts. In this case, the presence of a pole at \( s = 1 \) indicates that the system is unstable, as it does not meet the stability condition.
PREREQUISITESControl engineers, system analysts, and students studying control theory who need to understand the stability of LTI systems and apply BIBO criteria effectively.
dwsmith said:Can some show me how we show a LTI system is BIBO? I read the definition but it didn't help.
For example, how would we show if
\[
H(s) = \frac{s - 2}{(s + 2)(s + 1)(s - 1)}
\]
is BIBO stable or unstable?