Abstract

This article proposes a method to compute the maximum allowable delay time  for linear-time-invariant-time-delayed-systems (LTI-TDS) with state-PID feedback control. It presents the main theorem with corollary, and computing steps to obtain  Stability of a LTI-TDS with state- proportional integral derivative (PID) feedback is ensured if the delay time is less than  The proposed approach is compared with the matrix pencil method. Stabilization for the system is also proposed by using a low-pass filter. It was shown by simulation that the system is made more tolerable to delay by judicious selection of the DC gain and the time-constant of the filter. Seven case studies serve to demonstrate the effectiveness of the proposed approaches.

Key words: Routh’s criterion, time-delayed, state-PID feedback, stability and stabilization, neutral systems.