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On pole assignment in multi-input controllable linear systems

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1 Author(s)
W. Wonham ; Brown University, Providence, RI, USA

It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenberger's type for asymptotic state identification.

Published in:

IEEE Transactions on Automatic Control  (Volume:12 ,  Issue: 6 )