I'm having hard times with the following simple linear ODE coming from a control problem:
with a given smooth satisfying
for all .
My intuition is that , and that the convergence is exponential, i.e., .
For instance, if was a constant, then the exponential convergence clearly holds.
Do you see a simple proof for time-dependent (I'm getting grey, but could not prove it), or is my intuition wrong?
Many thanks, Peter