Consider the system: xi(t) = x(t) + 4x2(t), *2(t) = x(t) = x(t). (a) Find the...

 

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Consider the system: xi(t) = x(t) + 4x2(t), *2(t) = x(t) = x(t). (a) Find the equilibrium points and assess their stability using the Indirect Lyapunov Method. (b) Find constants a and b such that the Lyapunov function of the form V(x) = ax + br can be used in the Direct Lyapunov Method to prove stability of the equilibrium. (2) Consider the system: xi(t) = x(t) + 4x2(t), *2(t) = x(t) = x(t). (a) Find the equilibrium points and assess their stability using the Indirect Lyapunov Method. (b) Find constants a and b such that the Lyapunov function of the form V(x) = ax + br can be used in the Direct Lyapunov Method to prove stability of the equilibrium. (2)