B design the gain matrix k to meet the following

Question

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 ω_b ≥ 1 rad/s; and (iii) the steady-state error to a unit step input R(s) = 1/s is zero.