Consider the system of equations
Find a Lyapunov function to determine the stability of the equilibrium solution . Consider the three cases in your calculations: a) positive semidefinate, b) positive definite and c) negative definate.
If is positive semidefinite, then so the zero solution is uniformly stable.
If is positive definite, then so the zero solution is asymptotically stable.
If is negative definite, then so the zero solution is unstable.