Monodromy eigenvalue assignment in linear periodic systems

This note addresses the problem of assigning the eigenvalues of the monodromy matrix of a linear continuous-time periodic system by periodic state feedback. A controllability criterion is given which slightly strengthens known results. An explicit expression for a periodic feedback gain which performs the pole assignment is given. When the system is controllable over one period, the whole monodromy matrix is assignable by periodic feedback. An example is given.