<< Chapter < Page Chapter >> Page >
Explains bounded input, bounded output stability.

Introduction

BIBO stability stands for bounded input, bounded output stability. BIBO stablity is the system property that any bounded input yields a bounded output.This is to say that as long as we input a signal with absolute value less than some constant, we are guaranteed to have an output with absolute value less than some other constant.

Discrete time bibo stability

In order to understand this concept, we must first look more closely into exactly what we mean by bounded. A bounded signalis any signal such that there exists a value such that the absolute value of the signal is never greater than some value.Since this value is arbitrary, what we mean is that at no point can the signal tend to infinity, including the end behavior.

A bounded signal is a signal for which there exists a constant A such that n f n A

Time domain conditions

Now that we have identified what it means for a signal to be bounded, we must turn our attention to the condition a systemmust possess in order to guarantee that if any bounded signal is passed through the system, a bounded signal will arise on theoutput. It turns out that a continuous-time LTI system with impulse response h n is BIBO stable if and only if it is absolutely summable . That is

Discrete-time condition for bibo stability

n h n

Z-domain conditions

Stability for discrete-time signals in the z-domain is about as easy to demonstrate as it is for continuous-time signals in theLaplace domain. However, instead of the region of convergence needing to contain the j ω -axis, the ROC must contain the unit circle. Consequently, for stable causal systems, all poles must be within the unit circle.

A stable discrete-time system.
An unstable discrete-time system.

Bibo stability summary

Bounded input bounded output stability, also known as BIBO stability, is an important and generally desirable system characteristic. A system is BIBO stable if every bounded input signal results in a bounded output signal, where boundedness is the property that the absolute value of a signal does not exceed some finite constant. In terms of time domain features, a discrete time system is BIBO stable if and only if its impulse response is absolutely summable. Equivalently, in terms of z-domain features, a continuous time system is BIBO stable if and only if the region of convergence of the transfer function includes the unit circle.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Signals and systems' conversation and receive update notifications?

Ask