Symbolic Eigenvalue Assignment with Matlab Symbolic Math Toolbox

I tried to use the Symbolic Math Toolbox and the Control System Toolbox to compute an observer gain depending on some variables T and C as shown here:

% Define variables
syms T
syms C

% Define system matrices
Phi = [1, -T/(2*C), -T/(2*C);...
       0, 1, 0;...
       0, 0, 1];
C = [1, 0, 0;...
     0, 1, 0];

% Specify eigenvalues
syms p1 real;
syms p2 real;
syms p3 real;

p = [p1, p2, p3];

K = place(transpose(Phi), transpose(C), p);

Error using sym/svd (line 110)
Input arguments must be convertible to floating-point numbers.

Error in place (line 121)
[T,Gamma,Sj] = svd(U1'*(P(i)*I-A));
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

However, I geht the error that the SVD used within place is only capable to handle floating-point values.

I was surprised that there is a problem with the SVD function as there is one in the symbolic toolbox as well.

So, my question is: Is it possible to apply the place method with symbolic variables?

I found a workaround to calculate the gain via the characteristic poynomial but my hope was not to have to take this detour.

[Torsten]

So, my question is: Is it possible to apply the place method with symbolic variables?

No, there isn't.

Answer 1

[Christine Tobler]

It seems that the svd function in Symbolic Toolbox supports the one-output syntax in general, but only supports the 3-input syntax for inputs that can be converted to floating-point values.

The eig function supports returning the eigenvectors, too, so one workaround would be to compute eig([0 A; A' 0]) instead, from which the singular values and singular vectors can be extracted.

However, another possible problem is that eig on a symmetric matrix, in Symbolic Toolbox, returns eigenvectors which are not orthonormal to each other. It's very possible that the code in place relies on the singular vectors being orthonormal.