Consider the single-input, single-output system as described by
x(t) = Ax(t) + Bu(t)
y(t) = Cx(t)
where

Assume that the input is a linear combination of the states, that is,
u(t) = -Kx(t) + r(t),
where r(t) is the reference input. The matrix K = [K1 K2] is known as the gain matrix. If you substitute u(t) into the state variable equation you will obtain the closed-loop system
x(t) = [A - BK]x(t) + Br(t)
y(t) = Cx(t)
For what values of K is the closed-loop system stable? Determine the region of the left half-plane where the desired closed-loop eigenvalues should be placed so that the percent overshoot to a unit step input, R(s) = 1/s, is less than P.O.

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