State_space_Obsevability_Controlability2

For 4 questions AUD$60
Q1,Q4, and Q5 is atachmnet
Q2
Examine the state space model of the inverted pendulum write
MATLAB code to
(1) Design a state observer such that the poles of the observer are -1,-1.5,-2,-2.5.
(2) Design state feedback control law u=-Kx such that the poles of the closed-loop system are
-2, -3, -4, -6 (as in Assignment 1 Question 1). Describe the state-space model of the
closed-loop system including the observer and feedback control.
(3) Simulate the state trajectory of the closed-loop for any given initial states.
Refence question
Examine the state space model of the inverted pendulum in Part 2 of Week 1 Tutorial exercises
(https://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemMo
deling), and answer the following questions:
(1) Check the stability and the controllability of the system;
(2) Design state feedback control law u=-Kx such that the poles of the closed-loop system are
-2, -3, -4, -6. Show the state trajectory and output trajectory in MATLAB for a given
initial state.

See Q1, Q4, Q5 in attached file