BIBO stability

BIBO stability ( from English- bounded input, bounded output), also Eingangs-/Ausgangs-Stabilität, is a term from systems theory and control engineering. The stability of a system is guaranteed if the output does not grow with limited input signal across all borders. Stable systems may be physically realized on the basis of the conservation of energy to indicate no saturation effects.

For the definition of stability, there are different methods, in the system theory, the so-called BIBO stability is common. It is in this case, made ​​a restriction to linear time-invariant systems, so-called LTI systems in the form of continuous and discrete-time systems.

Definition

An LTI system is BIBO stable then when it responds to every bounded input function and every bounded input sequence with a limited output function or with a limited output sequence. A function is then limited if the amount is small for all time as a fixed barrier:

Similarly, a bounded sequence satisfies the condition:

A system is then BIBO stable if and only if a finite constants:

Or for discrete systems:

Impulse response

The BIBO stability of a LTI system can also be about whose impulse response expressed when it is absolutely integrable:

For discrete-time LTI systems is considered analogously: