Items tagged with linearize


Dear all,

I have to differential equations that I'd like to linearise, that is all higher order (>1) derivatives (like diff(uu[0],x$2)) and parameters (like beta^2) and the products of any derivatives with the parameters uu[0] and beta are zero (as they are assumed small).

The two equations considered are displayed below:


Up to now, I perform a very tedious substitution which is based on looking at the equations above and decide which terms I want to get rid of. Something like this, where K =1:KFBCLin:=simplify(eval(KFBC, [beta^3 = 0, beta^2 = 0,
seq(subs((diff(uu[n], x$3)) = 0),n=0..K),
seq(subs((diff(uu[n], x$2)) = 0),n=0..K),
seq(subs((diff(uu[n], t))*beta = 0),n=0..K),
seq(subs((diff(uu[n], x))^2 = 0),n=0..K),
seq(subs(g*diff(beta, x)*beta = 0),n=0..K),
seq(subs((d^2*diff(uu[n], x,t)*diff(beta,x)=0)),n=0..K),
seq(subs(-2*d*diff(uu[n], x,t)*beta*diff(beta,x)=0),n=0..K),
seq(subs((d^2*diff(uu[n], x$2,t)*beta=0)),n=0..K),
seq(subs((diff(uu[n], x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*beta)=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*d)=0),n=0..K),
seq(subs((diff(beta, x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*beta)=0),n=0..K)]));As there is a lack of automatisation, this procedure is not very helpful. Life would be easier if there was a command (or the like) that says "get rid of higher order derivatives".Any help is appreciated.Best regards,

MapleSim already developed a Template for Linearization.

The code behind "Linearize" button in the Linearization template is as follows:


The results, namely A,B,C,D matrices in the state-space presentation, are shown in the text area "mcEqs".

How can I save these matrices to some variables for further analysis?

In addition, without the linearization template, 

Hello all,

I'll be straight-forward.

I have Maple 15+MapleSim 5. I don't have Control Design Toolbox. I want to embed a linearized system object as an msys file into MapleSim.

The Linearization template failed to create the file. I tried to use the codes in the template directly as code in Maple, but also failed. Seemingly because I don't have Control Design Toolbox in which the code need to load.

I have been googling around with no avail. I...


I have linearized the following system and I want to extract the linear matrices (a,b,c,d) form the solution. The program is as follows:


I am trying to linearize a Statespace and extract the linear matrices from the solution. Using following example, can you explain how to extract the matrices a,b,c,d.


Is there any command in Maple 15 to linearize an PDE non-linear? Or or there is a package or help file to do so?


I'm handling with Non-linear PDEs in my work and I would like to solve them by these methods.



Thank You


Washington Inacio






I am in need of help with Maple Linearize and an exremely crypitc and most un-helpful error message. What does this mean:

> linmod := Linearize(syss, parm, linp);
Error, invalid input: Linearize uses a 4th argument, linpoint (of type {list(`=`), set(`=`)}), which is missing

I can find nothing in the help in this.

Linearize works fine when running a sample program from the help files, but fails when I run my equations.  

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