Controllability, Feedback and Pole Assignment
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 101)
Consider as usual the system
Suppose we are free to modify (1) by setting
$$ \dot x\left( t \right) = Ax\left( t \right) + Bu\left( t \right),t \geqslant 0. $$
where v(.) is a new external input, and F: χ → u (is a constant map. We refer to F as the state feedback. The obvious result of introducing state feedback is to change the pair (A, B) in (1) into the pair (A +BF, B). We shall explore the effect of such a transformation of pairs on controllability and on the spectrum of A+BF. Our main result is that if (A, B) is controllable then σ(A +BF) can be assigned arbitrarily by suitable choice of F, and this property in turn implies controllability.
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Notes and References
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