Question: Given the first order nonlinear system with input, u(t): x = x3 + u . Linearize the system at the origin and write the state

Given the first order nonlinear system with input, u(t): x = x3 + u . Linearize the system at the origin and write the state equations: x = ax + bu, then apply state variable feedback and determine the range of k that results in a stable system. What is the region of attraction (use set notation)? Remember this is a linear system now. . Apply the same state feedback control law of part (a) to the nonlinear system and determine the region of attraction. Let V(x) = =x2. Determine where V

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