Consider the system is described in state variable form by
Assume that the input is a linear combination of the states, that is,
(a) Obtain the characteristic equation associated with A-BK.
(b) Design the gain matrix K to meet the following specifications: (i) the closed-loop system is stable; (ii) the system bandwidth ωb ≥ 1 rad/s; and (iii) the steady-state error to a unit step input R(s) = 1/s is zero.