In this paper, we present an application of a semi-discretization method to the stability and robust analysis of optimally designed PID feedback control of a periodic linear system with time delay. The semi-discretization method uses a mapping of the system response in a finite-dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. The robust analysis examines the stability region of system parameters with modeling errors when the control gains are set to be the optimal ones. Extensive numerical examples of stability regions are presented in the paper.

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