Bibo Stability

In Electrical Engineering , specifically Signal Processing and Control Theory , BIBO Stability is a form of Stability for Signal s and systems. BIBO stands for ''Bounded-Input Bounded-Output''. If a system is BIBO stable then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value $B > 0$ such that the signal magnitude never exceeds $B$ , that is
	:<math>\ \int {-\infty}^{\infty}{\lefth(t) Ightdt}	\ h \_{1} < \infty</math>

Let <math>\ X \ {\infty}</math> Be The Maximum Value Of <math>\ x "n" class="copylinks" target="_blank">{Link without Title} </math>, ie, the Infinity Norm
:<math>\lefty[n] Ight \left\sum_{k=-\infty}^{\infty}{h[n-k] x[k]} ight</math>

So If <math>\ X \ {\infty} < \infty</math> (ie, It Is Bounded) Then <math>\lefty "n" class="copylinks" target="_blank">{Link without Title} ight</math> is bounded as well because <math>\ x \_{\infty} \ h \_1 < \infty</math>
::<math> \int_{-\infty}^{\infty}{\lefth(t) ight \left e^{-j \omega t} ight dt}</math>
::<math> \int_{-\infty}^{\infty}{\lefth(t) (1 \cdot e)^{-j \omega t} ight dt}</math>
::<math> \int_{-\infty}^{\infty}{\lefth(t) (e^{\sigma + j \omega})^{- t} ight dt}</math>
::<math> \int_{-\infty}^{\infty}{\lefth(t) e^{-s t} ight dt}</math>

Where <math>z r e^{j \omega}</math> and <math>r = z = 1</math>

	CATEGORIES ABOUT BIBO STABILITY

	control theory

	signal processing

	digital signal processing

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Bibo Stability