Stability analysis and control of linear periodic time-delay systems with state-space models based on semi-discretization

Stability analysis and control for linear periodic time-delay systems described by state space models are investigated in this paper. Semi-discretization method is used to develop a mapping of the system response in a finite-dimensional state space. The stability region and stability boundary can be found by comparing the maximum absolute value of the mapping's eigenvalues with 1. More importantly, an efficient stability criterion is presented for linear periodic neutral systems. Besides, minimization of the maximum absolute value of the mapping's eigenvalues leads to optimal control gains. Two numerical examples are given to illustrate the proposed method's effectiveness.