# [Maxima] Two questions

Zbigniew Komarnicki cblasius at gmail.com
Mon Jul 12 14:35:43 CDT 2010

```On Monday 12 of July 2010 17:14:22 you wrote:
> Zbigniew,
>
> there is << (quote) the package COMA (COntrol engineering with MAxima)
> COMA is a well designed package for (wx)Maxima. It has functions for
> studies of linear continuous systems in the time domain and Laplace domain.
> It contains state space methods and functions for optimizing and computing
> stability limits and stability areas.
> The newest version can be found at>>
>
> http://sourceforge.net/apps/phpbb/maxima/viewforum.php?f=3
>
> It comes withe a very fine documentation.
>
> best
> Wolfgang Lindner

Thank you very much I do not know about it.  It is very useful :-)

But I still search for software for symbolic matrix - vector - scalar
manipulations/computations. This package above is very useful for people who
work with concrete values in their matrices, vectors or polynomials, but I
want to work only on symbolic matrix vector scalar manipulations. I currently
work on ILC (iterative learning control) system, where I have to  manipulate
on equations of vector - matrix such as those below (where big letters
denotes matrices and small letters denotes vectors):

eq: e(r+1, k+1) =  (I-C.B.K2) . e(r, k+1) - (C.B.K1 + A.C) . z(r+1, k)

above I obtain closed loop system and then I want to use Lyapunov function to
derive LMIs (Linear Matrix Inequalities) to compute K1 and K2 from LMIs.

Currently in maxima I can obtain only similar result when I use operator "*"
instead of '.', because no simplification is made and the order of matrices
is not preserved.

When I use operator '.' I got:
e(r+1, k+1) = - C.B.K2 . e(r, k+1) - C.B.K1 . z(r+1, k)
- C.A . z(r+1, k) + e(r, k+1)

I know that in such simple example there is no problem, but when we have e.g.
50 or more matrices there is a problem and I want to use maxima for this
cases.

Thank you.

Zbigniew
```