Question: Question 3. Consider a MISO system x(t) = Ax(t) + Bu(t), (1) y(t) = Cx(t), (a) Determine the controllability and observability of the system. (b)

Question 3. Consider a MISO system x(t) = Ax(t) + Bu(t), (1) y(t) = Cx(t), (a) Determine the controllability and observability of the system. (b) Consider a single input v(t) E R and generate the actual system input as u (t) = BV(t) (2) where B is a column vector. Write the state equation of the equivalent SISO system ob- tained by combining (1) and (2). (c) Given a characteristic polynomial of the closed-loop system, find a state feedback gain K for the single-input control law v(t) = Kx(t)

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