Consider the single-input, single-output system 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. Substituting u(t) into the state variable equation gives the closed-loop system
x(t) = [A - BK]x(t) + Br(t)
y(t) = cx(t)
The design process involves finding K so that the eigenvalues of A-BK are at desired locations in the left-half plane. Compute the characteristic polynomial associated with the closed-loop system and determine values of K so that the closed-loop eigenvalues are in the left-half plane.

Transcribed Image Text:

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