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.