can we solve linear matrix inequalities by using only matrix forms?

I have LMI problem. Is there any tool to solve it just by using Matrix forms. For example I want to solve Ax>b for x. So I just initialize matrix A and vectro b and then find x. because to write LMI not in matrix from it needs approximately 16 lines, which is a lot of time

[Torsten]

What do you mean by "solve Ax>b for x" ? Usually, there are infinitely many such x.

[Otankhan]

I tried to simplify what i want to ask. but it didn't work. I have system of linear matrix inequalities. one is 16*16 matrix. other 2 are 2*2.

[Otankhan]

do you have gmail? so i can show my problem there?

[Matt J]

I get the sense that you are not using the terminology "Linear Matrix Inequality" as described here,

https://en.wikipedia.org/wiki/Linear_matrix_inequality

If you were, then you should have mutiple A matrices.

[Otankhan]

it was just wrong example, but yes my problem is about finding A

[Matt J]

But you said above that you want to find x? If that's still what you want, please engage the answer below. Otherwise, edit your original post to clarify what you want.

Answer 1

[Matt J]

As Torsten says, A*x>b generally corresponds to not one x, but an entire polyhedral region of them. However, if the region is bounded, you can obtain the vertices of the region by downloading,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra

xVertices=lcon2vert(-A,-b);