Consider the system *1 = -x2 + ax1x2, x = x-bxx2, ab. (3) (a) Use the...

 

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Consider the system *1 = -x2 + ax1x2, x = x-bxx2, ab. (3) (a) Use the Indirect Lyapunov Method to show that there is a single equilibrium point and to assess its stability. Is the equilibrium point stable / unstable / impossible to conclude due to linearization failure? (b) Let's use the Direct Lyapunov Method. Consider the Lyapunov function candidate V(x) = x + 2. Show that V is a Lyapunov function for the system. Then the equilibrium point is asymptotically stable if and only if function F(a, b) <0. What is F? Consider the system *1 = -x2 + ax1x2, x = x-bxx2, ab. (3) (a) Use the Indirect Lyapunov Method to show that there is a single equilibrium point and to assess its stability. Is the equilibrium point stable / unstable / impossible to conclude due to linearization failure? (b) Let's use the Direct Lyapunov Method. Consider the Lyapunov function candidate V(x) = x + 2. Show that V is a Lyapunov function for the system. Then the equilibrium point is asymptotically stable if and only if function F(a, b) <0. What is F?