Consider the system described by the matrices A=[0 1 0; 80 0 -2.8; 0 0 -100], B=[0; 0, 100], C=[1 0 0] and sampled ev

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Consider the system described by the matrices A=[0 1 0; 80 0 -2.8; 0 0 -100], B=[0; 0, 100], C=[1 0 0] and sampled every 10ms. Analyze the stability of the system and show its behavior through simulation, considering its natural response. Design a state feedback controller considering continuous closed loop poles (-10 + 10i, -10 – 10i, -50). Verify the stability of the new closed-loop system and carry out a simulation in which its follow-up response to a unit step is observed. Design an observer of states whose poles are about 10 times faster than the slowest pole. Run a simulation looking at its performance when tracking a square pulse signal. Implement the system, controller, and observer using TrueTime. Submit a short report (pdf) in addition to the simulation files that allow corroborating compliance with what is entrusted.