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matlabmathematical-optimization

H infty optimization of transfer function matrix

I have a two-dimensional (2 x 2) transfer function matrix like this:

enter image description here

The aim is to solve optimization problem:

$$\min_{x, y} ||G||_\infty $$

I used this code, but there is sth wrong:

   syms s
   s = tf('s');
   x = fmincon(@(x) norm([1/(x(1)*s+1), 1/(s+0.5); 3/(s+3), 1/(x(2)*s+2),inf),[1 1],[],[],[],[],[0 0],[2 2])

How can I treat this optimization problem?

Solution

  • The error is:

     x = fmincon(@(x) norm([1/(x(1)*s+1), 1/(s+0.5); 3/(s+3), 1/(x(2)*s+2),inf),[1 1],[],[],[],[],[0 0],[2 2])
                                                                          |
Error: Unbalanced or unexpected parenthesis or bracket.

    which is pretty clear. You forgot to close a bracket. It should be:

    norm([1/(x(1)*s+1), 1/(s+0.5); 3/(s+3), 1/(x(2)*s+2)],inf)

    Also, you don't need syms s, s = tf('s') is enough.