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?
Bounded Output Bounded Input (BIBO) is a concept in control systems theory that refers to a system's ability to produce an output within a certain range when given an input within a certain range. It is used to analyze the stability of a system and determine if it will produce a stable output for a given input.
BIBO can be tested by plotting the input and output signals of a system on a graph and ensuring that the output remains within a certain range for all values of the input. Another method is to use mathematical analysis to determine if the system's transfer function satisfies the BIBO stability criterion.
BIBO is important because it allows us to predict and control the behavior of a system by analyzing its inputs and outputs. It is particularly useful in engineering and control systems design, as it helps ensure that a system will produce a stable output for a given input.
No, a system cannot be both BIBO stable and unstable at the same time. If a system is BIBO stable, it means that it will produce a stable output for a given input. If a system is BIBO unstable, it means that its output will become unbounded for certain inputs, which is not considered stable.
BIBO stability differs from other stability criteria, such as absolute stability and asymptotic stability, because it only considers the input and output signals of a system. Other criteria may take into account internal states or the behavior of the system over time. BIBO stability is a more conservative criterion, as it only guarantees stability for a finite range of inputs and outputs.