Let the state feedback be defined as u(t) = r(t) Ks(t), where K = [k1 k2]. Obtain the state space equation for the closed loop system. What matrix A for the closed loop system?

I do not know How to deal with (c) and (f)

I do not know How to deal with (c) and (f)

Problem: Consider the following input-output transfer function: Y (s) 2s2+s+5 U(s) s3+ s2+11s+4 (a) Obtain the state space equation for the above system in the controllability canonical (b) Obtain the state space equation for the above system in the observability canonical (c) Let the state feedback be defined as u(t) r(t) - Ks(t), where K [k k2]. Obtain the form. Draw the corresponding signal flow graph. form. Draw the corresponding signal flow graph. state space equation for the closed loop system. What matrix A for the closed loop system? (d) What is the observability matrix (in terms of k, and k2) for the closed-loop system? (e) What is the controllability matrix (in terms of k and k2) for the closed loop system? (f) Find k1 and k2 for the system to be both controllable and observable