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Pole placement problem Previous Next Contents

1.iii. Pole placement problem

Suppose now that we wish to control the system of the previous section with constant linear output feedback y = Fu:
The behaviour of the closed system
dx/dt   =   (A + BFC)x
is determined by the roots of the characteristic polynomial
f(s) = det(sIn - A - BFC).
   This is the forward problem: Given a system, represented as matrices A,B,C, and a feedback law F, the system evolves according to the behaviour encoded in its characteristic polynomial f(s). The inverse problem is the

Pole Placement Problem:
Given a linear system represented by matrices A,B,C, and a desired behaviour f(s), which feedback laws F satisfy f(s) = det(sIn - A - BFC)?
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