On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

This study provides some methods to analyze robust stabilizability of uncertain plants with an uncertain time delay using arbitrary linear controllers. In this work, an uncertain plant with an uncertain time delay means that the numerator and denominator coefficients and the time delay term of the transfer function of the plant have interval uncertainties. Towards solving the abovementioned problem, first, robust stability is investigated for the closed-loop system in terms of a general class of linear controllers and uncertain plants with an uncertain time delay. Then, by using some interesting geometric features, a robust stability checking function and frequency bounds are provided to improve the computational efficiency of robust stability analysis. Furthermore, due to the widespread industrial use of the well-known proportional–integral-derivative (PID) controller structure, the robust stability region of PID controllers has been determined for an uncertain plant with an uncertain time delay. Finally, two numerical examples are given to verify the obtained results.