Talk:Linear system

Causal property

Should the causal property be included here?

Not all linear systems are causal. Not all causal systems are linear. —Preceding unsigned comment added by CSears (talk • contribs) 23:14, 21 September 2007 (UTC)

is the current statement wrt causality correct? -Happyseaurchin (talk) 12:22, 14 December 2011 (UTC)

Definition very unclear

The article says a linear system "can be described" by a linear operator H that maps x(t) to y(t). But the article doesn't say HOW the linear operator H is used to describe the system, and it doesn't say what x(t) represents or what y(t) represents (other than calling them the "input" and the "output" which is uninformative). Does x(t) represent the state of the system? Does y(t) represent the state of the system? How do I find x(t+1) given x(t)? The rest of the article never even mentions H again.

AT MINIMUM the article needs a physical example of a linear system using the same notation H, x(t), and y(t). Halberdo (talk) 04:34, 1 December 2012 (UTC)

Reviewing some reverts

This was recently posted to my talk page. I would appreciate some help from other editors in resolving this. ~KvnG 13:45, 12 May 2014 (UTC)

Hi,

Thank you for reviewing my changes to linear systems

https://en.wikipedia.org/w/index.php?title=Linear_system&oldid=prev&diff=607022811

However I think the current version is really confusing. You reverted the changes based on the idea that I was introducing a different y(t). But that is :not the case if you look at the two equations that use y_1 and y_2. If you think the linear spring as the linear system, then these y_1 and y_2 are the :applied forces and that was exactly the y(t) I introduced. Additionally the condition "Letting y(t) = 0" is completely unnecessary and indeed confusing... What is the output then? if it is supposed to be always 0?

The spring viewed as a input-output linear system in the way the example wants to show it is indeed a system that maps trajectories (inputs) into forces (outputs). In this sense I think my explanation is far more consistent that the current one. Can we have an explanation that rescue the best of both versions?

Thanks Kakila (talk) 16:43, 11 May 2014 (UTC)

What about

For example, a forced harmonic oscillator obeys the differential equation:

$m{\frac {d^{2}(x)}{dt^{2}}}+kx=y(t)$

Where $y(t)$ is the applied force.

If we consider an operator H of the form

$H(x(t))=m{\frac {d^{2}(x(t))}{dt^{2}}}+kx(t)$,

We can rewrite the differential equation as $H(x(t))=y(t)$, which shows that H is a linear system that maps trajectories of the harmonic ::oscillator into applied forces (this operator is called inverse dynamics in control theory).

Kakila (talk) 11:43, 22 May 2014 (UTC)

Don’t understand this section. Any chance of expanding to explain the reasoning? Rhodydog (talk) 02:40, 7 February 2024 (UTC)

Inappropriate title

"Linear system" has a wide usage in mathematics and does not specify this particular application, The usual term is "linear systems analysis" or a little more precisely, "linear systems-analysis". JFB80 (talk) 15:37, 24 January 2016 (UTC)

Incrementally linear system

I couldn't find any info about incrementally linear systems. Just an idea for expanding the article. Dalba 11:59, 2 January 2019 (UTC)

"Incrementally linear system" seems not belong to the standard terminology. Do you have a definition or a source where this phrase is used? D.Lazard (talk) 14:02, 2 January 2019 (UTC)