I am interested in finding the DIFFERENCE in the state space distributions for two linear dynamical systems (System A and System B).
I am able to solve for this using the matrix exponential.
But the formulas become very unweildly. I was wondering if there might be another approach to this problem that yields a nice compact formula, that might even eliminate some variables?
Cheers
Mark
System A:
Rate Matrix System A:
$\left[ \begin{array}{c c c} -(a+b) & a & b\\ 0 & -g & g\\ 0 & 0 & 0 \end{array} \right]$
Initial State System A:
$\left[ \begin{array}{c} A(0)\\ 1-A(0)\\ 0\end{array} \right]$
System B:
Rate matrix System B:
$\left[ \begin{array}{c c c} -(a+b \beta) & a & b\beta\\ 0 & -g & g\\ 0 & 0 & 0 \end{array} \right]$
Initial State System B:
$\left[ \begin{array}{c} A(0)+d\\ 1-A(0)-d\\ 0\end{array} \right]$