## 50 Reputation

11 years, 264 days

## Solving Lyapunov equations...

Maple

When executing "P, k := LyapunovSolve(A, C)" command, I got the following warning:

"Warning, Matrices have common or very close eigenvalues; perturbed values were used to solve the equation"

Although Maple can give the solution, P and k don't satisfy the equation:

A.P+P.A^%T-C = 0        (1)

Are there any other ways to solve the Lyapunov equation (1)?

## Linearization tool in API...

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,

## Can't apply 2 proposal methods...

I have another differential equations that I can't find the integral of its solution by applying above 2 methods. Maple runs more than 10 mins without results. These equations are attached in this comment.

I really appreciate all your help.

DAEs_solver.mw

## how to solve differential algebraic equa...

Maple 15

Hi all,

I try many ways to solve the below DAEs, for example stiff=true, method = rkf45_dae, method=rosenbrock..., but my DAEs can't be solved. In different ways, there are different errors, such as "Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up", ""

Would you please show me how to solve the below DAEs and plot their solutions?

I really appreciate your help.

## integral of solution of differential equ...

Maple 15

Hi all,

I have a differential equation as follows:

x(t)^2+cos(x(t))+diff(x(t), t)+diff(x(t), t, t) = 100

x(0)=2, D(x)(0) = 3;

After using "dsolve" to solve this equation, the solution x(t) is obtained.

How can we obtain the following function?

g(k) = 0kx2(t)dt

How can we plot the function g(k...

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