BIBOstable

BIBOstable is a term used in control theory to describe a system that is bounded in its output for bounded inputs. The acronym BIBO stands for Bounded Input, Bounded Output. This means that if the input signal to the system remains within a certain range, the output signal will also remain within a certain range and will not grow indefinitely.

A system is considered BIBOstable if and only if all of its poles lie strictly in the left half of the complex plane. Poles are the roots of the denominator of a system's transfer function. The presence of poles on the imaginary axis or in the right half of the complex plane can lead to instability. For example, if a system has a pole at the origin (zero frequency) or in the right half-plane, even a small, sustained input can cause the output to grow without bound.

BIBO stability is a fundamental concept in the analysis and design of control systems. It is a necessary condition for a system to be considered well-behaved and predictable. If a system is not BIBOstable, its response to even small disturbances can be extreme, making it unsuitable for many practical applications. Understanding and ensuring BIBO stability is crucial for engineers working with dynamic systems. The concept is particularly relevant in fields like electrical engineering, mechanical engineering, and aerospace engineering.