Talk:Linear system

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Not an adequate discussion?[edit]

This is not really an adequate discussion, considering the importance of the topic.

Charles Matthews 20:29, 18 Jun 2004 (UTC)

Why don't you improve it? Nixdorf 20:42, 18 Jun 2004 (UTC)

Well, you know, I arrived here by redirecting a link to it. So I'm busy with other things. Charles Matthews 20:46, 18 Jun 2004 (UTC)

I agree.. the article seems to well start to answer the question "What is it used for"; whereas the

description of "What a Linear System is" seems too shallow... This line seems strange.. "The mathematical properties of linear systems will typically include differential equations,".. It seems an artificial an uh property... DEs and Linear Systems are still different concepts, aren't they? Mysidia 20:48, 18 Jun 2004 (UTC)

I want to revise my knowledge about control systems by answering for these questions : 1 – (( choose the correct )) For a second order system sketch the response of the system to a unit step input , including on the sketch thetime domain specifications ( rise time , settling time , peak time , delay time over shoot ) ?

2 – What the meaning for these terms :

rise time, peak time

settling time

delay time over shoot

3 – What do we mean by the frequency response ( F.R.) of the system? state the types of techniques that are used in F.R.?

4 – What is a compensator in the control system ?

5 – Define the gain margin and the phase margin ?

6 – What do we mean by PID controller ?

7 – wht do we mean by stable system, marginally stable , and unstable system ?

8 – for the system shown , find the time-constant of the closed loop system ?

G (s) = 10 / ( S + 10 ) & H(s) = 0.04 S

9 – Given k G(s) = k/ { S ( S + 2 ) ( S + 4 ) } Find the range of k that makes the system stable? What is the angular frequency of the system at the maximum stable gain ?

10 – For a unity feedback control system, given

KG(s)= K (S+6)/ {S(S+4)} - sketch the root-locus for this system ?

11 – Given G(s)= 2/ { S(S+2) } & H(s) = (S+4) jhghg

12 - Find the damping ratio and the natural frequency of the system

And if...[edit]

...some kid comes here expecting to find homework help, will he/she find it? Probably not.

I second that. I have read some mathematics on a college level, and this just left me confused. Some simple everyday examples to show what a linear system is and isn't, please? Nirion (talk) 14:24, 10 May 2010 (UTC)

Causal property[edit]

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 (talkcontribs) 23:14, 21 September 2007 (UTC)

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

Definition and example[edit]

I think the article could be improved if a "Definition" title was added just after the 1st paragraph, and an "Examples" section just before the first (current) chapter. Albmont (talk) 13:16, 27 February 2009 (UTC)


The link to "scaling" is a dismbiguation page. Should the correct link be to "scaling (geometry)"? DGERobertson (talk) 16:10, 21 January 2010 (UTC)

Definition very unclear[edit]

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[edit]

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 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)