mapping from one invariant subspace to another
Hello to everybody,
I am trying to find a constructive proof for the solution of a problem in control engineering, and I got stuck at some point for the last few days. The problem is as follows:
For a system defined in state space as:
There are defined subspaces and of that the rest of the problem deals with, with properties:
The problem is to find an st.
Of course, the first thing that comes to mind is to find st.
which satisfies the problem requirement as . However, such a method appears to be too "tight" (meaning that more freedom on is needed) for many examples from application.
Another idea is to find st.
then find a restriction of the resulting on subspace . But then my mathematical knowledge is limited on restrictions on linear operators.
In short, I am stuck at finding an elegant approach for the construction of . Any help and ideas on the topic would be of great help. Thanks in advance.