On robust stability analysis of interval time delay systems using delayed controllers

The focus of this research is to explore the robust stability of interval time delay systems that utilize delayed controllers. Specifically, the study assumes the use of a Proportional-Integral-Retarded (PIR) controller in conjunction with a first-order plus dead-time (FOPDT) model of the time delay system. The parameters of the system, including the gain, time constant, and time delay, are subject to interval uncertainties, which are a type of structured uncertainties for the plant model. To investigate the robust stability of the system, the study derives necessary and sufficient conditions, accounting for the presence of uncertainties. To facilitate the assessment of robust stability, the study also introduces a frequency range and robust stability checking function. Ultimately, the study aims to demonstrate the accuracy of its findings through the presentation of two numerical examples.