Question: Consider a twice differentiable, nonlinear system x (t) = f(x(t)) with equilibrium point xe, and its linearized time invariant form, x(t) = Ax(t), where x(t)

Consider a twice differentiable, nonlinear system x (t) = f(x(t)) with equilibrium point xe, and its linearized time invariant form, x(t) = Ax(t), where x(t) = x(t)xe. Prove that if the linearized system is exponentially stable, then there exist a ball B(xe) Rn where the nonlinear system is, also, exponentially stable

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