Hello,

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