Problem 6 Consider the following nonlinear system x = -3xx+2x2cos (x3) - 4x2x3 x = xcos(x3)...

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Problem 6 Consider the following nonlinear system x = -3xx+2x2cos (x3) - 4x2x3 x = xcos(x3) - xx2 - 3x1x3 x3 = 2x1x25x3 a) Investigate the stability of the equilibrium point (0, 0, 0) using linearization b) Investigate the stability of the equilibrium point (0, 0, 0) using a Lyapunov function V(x1, x2, x3) = ax + bx + cx Problem 6 Consider the following nonlinear system x = -3xx+2x2cos (x3) - 4x2x3 x = xcos(x3) - xx2 - 3x1x3 x3 = 2x1x25x3 a) Investigate the stability of the equilibrium point (0, 0, 0) using linearization b) Investigate the stability of the equilibrium point (0, 0, 0) using a Lyapunov function V(x1, x2, x3) = ax + bx + cx