The framework for linear periodic time-delay systems based on semi-discretization: Stability analysis and control

Stability analysis and control for linear periodic time-delay systems are investigated in this paper. In this framework, a semi-discretization method is used to develop a mapping of the system response in a finite-dimensional state space. With the mapping, the stability region and stability boundary can be identified by comparing the maximum absolute value of its eigenvalues to 1. More importantly, an efficient stability criterion is presented for periodic neutral systems. In addition, minimization of the maximum absolute value of the mapping's eigenvalues leads to optimal control gains. The tracking control problem is also discussed. Two numerical examples are given to illustrate the effectiveness of the proposed method.