Abstract
It has been shown that in the case of time-invariant finite-dimensional linear systems, the controllability and the pole assignability are equivalent, in the sense that arbitrary closed pole locations can be achieved by the state-variable feedback if and only if the open-loop system is controllable.
The present paper considers a class of nonlinear systems which are constructed by a cascade connection of a nonlinear block and a linear time-invariant finite-dimensional system, and shows that the specified degree of stability can be achieved by the state-variable feedback if and only if the open-loop linear subsystem is controllable.
It is also shown that the desired feedback matrix can be determined (not uniquely) by solving a quadratic matrix equation. As an application of the result, the paper considers a stability problem by means of output feedback and gives a unified design procedure of a compensator which achieves the specified degree of stability.
