Designing controller system

Question

Assignment:

Consider the following system whose state space representation is as follows:

a) Design a controller for the system, place the poles at s=-10 and s = -15± 5j.

b) Design (if possible) a full-order observer for the system. Place the observer poles at s= -20,-20,-20.

c) Using MATLAB, repeat part (a) and (b). Also check that the matrices A-BK and A-LC have the desired eigenvalues.

d) Using MATLAB, plot x₁,x₂,x₃, x₁,x₂ ,x₃ in the same graph. Note that the initial state of the system is (-3,-3,-3); the initial state of the observer is 0.