On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems

It is well known that for a linear system in state space form, controllability is equivalent to arbitrary pole assignment by state feedback. This brief points out that for a scalar high-order fully actuated linear system, the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account, that is, controllability cannot guarantee arbitrary pole assignment by state feedback.

Automated summary

In certain linear systems, the pole assignment problem can only be solved when the desired pole set of the closed-loop system does not include the zero set of the open-loop system, when considering the implementation issue of the controller. This means that controllability cannot ensure arbitrary pole assignment by state feedback.