Prove is an exponentially stable equilibrium of the system if
Besides the conditions in the title, we have:
1. is an exponential equilibrium of the system
2.
3. is sufficiently small!
What I have tried so far is that:
1.
2. We want to prove: such that
Considering the following system:
1.
2.
Then we will have:
1. such that
2. , and by Gronwall inequality
I have a sense that it might be somewhat close to what we want to get. And I am stuck at this stage.