EE611

Homework #29

Due Monday, December 1

1a) Find the gradient of

b) Find the Hessian matrix for problem 1a)

c) Find the Jacobian Matrix of

2a) Suppose a nonlinear system is modelled by:

Using perturbation theory, find a linearized model for the system about the operating point, x_nom= [0 1 0]^T and w_nom= [0 0]^T

b) Consider the following nonlinear system in nonlinear canonical form

Find a control which linearize the system and sets the eigenvalues of the linearized system to {-3,-4,-5}