Examine the state space model of the inverted pendulum in Figure 1 and answer the following questions. Click the following link to find the state space model (for reference only): https://ctms.engin.umich.edu/CTMS/index.php?example-Inverted Pendulum§ion SystemMo deling P M m,I Figure 1. Inverted Pendulum Assume that: (Vc) volume of the aluminium cart (Vp) volume of the aluminium pendulum (p) density of the aluminium (b) friction of the cart (1) (1) (F) (x) (0) length to pendulum inertia of the pendulum force applied to the cart cart position coordinate pendulum angle from vertical. 2000cm 600cm 2.7g/cm 0.5 N/m/s 0.3 m 0.01 kg*m (1) Check the stability and the observability of the system. (2) Design state feedback control law u = -Kx such that the poles of the closed-loop system are -4, -3, -5, -7. Show the state trajectory and output trajectory in MATLAB for a given initial state.