Pole assignment in descriptor periodic systems

In this paper a pole assignment problem is considered for the descriptor linear discrete-time periodic systems, which is using the periodic proportional-derivative feedback to modify a given system such that the closed loop system has a specified self-conjugate set of eigenvalues. It is shown that the complete reachability of an open loop periodic system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to the system by choosing the suitable periodic proportional-derivative feedback. A computational approach is also proposed to solve the problem, which uses the reliable numerical techniques based on the orthogonal transformations. Numerical examples are presented to illustrate the effectiveness of the proposed approach.