In this paper we present an application of a semi-discretization method to the stability analysis of PID feedback controls of linear systems with time delay. The method develops 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. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. The tracking control problem of linear systems with time delay is also discussed. We have found that the semi-discretization method provides accurate stability boundaries and performance contours in the parametric space of control gains, and offers an alternative to the classic design approaches of feedback controls.
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