I have this system:
(1)
I know that is asymptotically stable.
This is another system
where (2)
(i.e. the outer product of little
I know that system (1) is asymptotically stable iff system (2) is asymptotically stable.
How do I show that system (2) is stable (not necessarily asymptotically stable) iff there is a linear Lyapunov function proving it's stability. Note I said "linear Lyapunov function", not "quadratic Lyapunov function".
Also note is a nx1 vector, and are nxn matricies.