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The response of a linear and time invariant system to any input can be derived from its [[impulse response]] and [[step response]]. The eigenvalues of the system determine completely the [[natural response]] ([[unforced response]]). In control theory, the response to any input is a combination of a [[transient response]] and [[steady-state response]]. Therefore, a crucial design parameter is the ___location of the eigenvalues, or closed-loop poles.
In [[root-locus|root-locus design]], the [[Gain (electronics)|gain]], K, is usually parameterized. Each point on the locus satisfies the [[angle condition]] and [[magnitude condition]] and corresponds to a different value of K. For [[negative feedback]] systems, the closed-loop poles move along the [[root-locus]] from the [[open-loop poles]] to the [[open-loop zeroes]] as the gain is increased. For this reason, the root-locus is often used for design of [[proportional control]], i.e. those for which <math>\textbf{G}_c = K</math>.
==Finding closed-loop poles==
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