On Pole Assignment in Multi-input Controllable Linear Systems

Authors

W. Murray Wonham

Year

1967

Journal Paper

Algorithm

State Feedback Pole Assignment

Source

IEEE Transactions on Automatic Control

Identifiers

DOI 10.1109/TAC.1967.1098739

Abstract¶

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.

Summary¶

Wonham proves that controllability is equivalent to the ability to assign arbitrary closed-loop poles through linear state feedback in multi-input linear systems. The paper also links stabilizability to controllable unstable modes and gives the dual observer existence criterion, making it a compact foundation for modern state-space control synthesis.