BIBO Stability

[Archduke Tips]

Does anybody know how to figure out if a system is BIBO stable or not?
I found through the internet that it can be done by taking the integral from -infinity to +infinity of the magnitude of the transfer function for continuous time systems, but I am pretty sure this is not the method that my teacher intends us to use.

It seems like he wants us to solve these problems by intuition... but I have only seen one example of a BIBO stable system and one example of an unstable system, and I have trouble applying them to the homework problems that are assigned.

For example here is one of the systems from the homework that I need to determine if it is BIBO stable or not:

y(t) = dx(t)/dt + x(t)

I don't even know where to start on this one because of the 1st order DE. It looks to me like it is BIBO stable, but I have no way to prove it.

Anybody know how to do this?

[glowbelly]

smoke a joint first. it will alllllll make sense soon after.

[sadie]

bicky-bi-bo-bee-you-boo-bicky-bi-bo-boo

[Archduke Tips]

It turns out that my professor was intending us to solve the problems by intuition.

So the solution to y(t) = dx(t)/dt + x(t) would be that it is not BIBO stable because if you input the signal ln(t) you would get y(t) = 1/t + ln(t). At t=0 this signal will go to infinite.

I really like this class despite the fact that the homework is ridiculously hard.

[Archduke Tips]

Nevermind. I spoke too soon. The function ln(x) is in fact not bounded and so it is not valid to use for BIBO stability.

On second thought, I think that the system is BIBO stable!

[Dr. Fu]

skip a dap a doo

[ziggytrix]

Congratulations, you have almost acheived a degree of specialization to make a a worker bee look like a renaissance man.

Tell me, is BIBO stability interesting to you? Do you enjoy integrating and deriving functions?

Cuz I think Dif E sucks balls. I don't know how anyone can stand it. :(

[Archduke Tips]

It all comes with electrical engineering.

At this point I don't know enough about BIBO stability to judge whether it is interesting or not. Calculus and Differential Equations are second nature to me.

This particular course I am taking is Signals and Systems and it involves more math than you could shake a stick at!

[Juttin]

Specialization is for insects

He then got sued by a metal band full of 70 year olds.


THE END

[The One and Only...]

I would help, but I haven't learned how to do integrals yet. :(

[CaptainBubba]

edit: nevermind I see what your formula means. I'm playin with it now.

btw what is the domain we are dealing with as that heavily influences what is considered bounded?

And unless I'm mistaken ln(t) wouldn't be a bounded function as there is no M s.t abs(f(t)) < M. Again I could always be wrong so feel free to tell me if there is something I am missing.

[AChimp]

OAO, you are so far behind the math Russo is doing, it's ridiculous.

[ScruU2wice]

yeah it's like an eepeist facing off a level 54 ninja

[CaptainBubba]

Damnit I just re-read that you caught that ln(t) thing lol.

Stiiil need to know what the domain is. For now I'm assuming its just R.

Also I just read the OAO comment. Jesus fuck OAO, notr knowing integrals in college level math is basically the same as putting on leather chaps and a pink mustache then walking into a church and masturbating in the baptismal pool.

[CaptainBubba]

Ok I believe that your function is in fact BIBO stable. I have to study for history so I cant write a real proof or anything but here is my basic idea:

Given any bounded function
f(x) there must then be a maximal derivative
f'(tmax) != infinity
Then for all t on f'(t) we have f'(t) <= f'(tmax)
and so f'(t) is then bounded
and y = f'(t) + f(t) is then the sum of two bounded functions
and therfore bounded.

Note that proofs are my worst area in math. :( I'm more of a linear algebra guy.

Predicatably enough taking the integral from -infinity to infinity wqould basically involve the exact same logic, this just came to me first.

[camacazio]

I'm more of a linear algebra guy.

WHY DON'T YOU JUST GO SOLVE FOR AN EIGENVECTOR LOSER

[Sethomas]

I'm terrible at math, but my main problem has been that I get kicked out of school before I have a chance to take the final for my math classes. I'll be taking differential equations either next semester or in the summer, and linear algebra in the summer as well.

I screwed myself over by screwing up my placement exam and getting put into an amalgamated Calc I/II class, where we spent the first 8 weeks doing really mundane easy shit I learned in high school, and in the second eight weeks we had to learn everything from improper integrals to Maclauran series to converting functions to power series. I'd probably have done better if I actually studied harder, but oh well. There's a strong possibility I'll have to take the Calc II part again, but that'd probably be for the best.

Fuck me for double-majoring in Physics and Religious Studies.

[Archduke Tips]

Captain Bubba, we are dealing in the continuous time domain, but I think you figured that out.
I like your proof. So are a math major or an engineer or what?

[ziggytrix]

fuck your engineering math. combinatorics is so much cooler.

[CaptainBubba]

I am a math major and a comps sci major. I'm glad you like my proof! Always makes me happy when I do somethin people like.

And Camacazio, WHY DONT YOU GIVE ME A GOD DAMN nxn MATRIX THEN MOTHER FUCKER.

I mean it doesn't have to be nxn or anything but if its nxn I could premptively find a diagonalization. :(

[camacazio]

You SON of a BITCH

[3 2 2]
[1 4 1]
[-2 -4 -1]

[The One and Only...]

Also I just read the OAO comment. Jesus fuck OAO, notr knowing integrals in college level math is basically the same as putting on leather chaps and a pink mustache then walking into a church and masturbating in the baptismal pool.

Um. I'm a junior in high school.

[CaptainBubba]

So in terms of my analogy your defense is that you aren't a Christian.

[The One and Only...]

Any defense that lets me desecrate churches is automatically true by virtue of my decree, for, truly, I am God.

[Seven Force]

Fuckin' king of da jews!

Engineering? I was thinking about taking that. If that's what you're talking about, it sounds pretty difficult. :/

Edit: That's Jesus. My bad.