Stability of linear delayed systems subjected to digital control is analyzed. These systems can typically be written in the forṁ where t j = j∆t with ∆t being the sampling period for the digital controller. The point-delay term x(t − τ ) is assumed to be inherently present in the governing equation of the uncontrolled system, while the term x(t j−1 ) is present due to the digital controller. Since the term x(t j−1 ) can be represented as a term with a piecewise linearly varying time delay, the

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... ystem is time-periodic at period ∆t. The stability analysis for the system is performed using the semi-discretization method. As case studies, the stability charts of the delayed oscillator and the turning process are determined for a digital PD controller.