Robust Stabilization of Systems with Time varying Input Delay using PI State feedback Controller

Abstract

Time delays are often encountered in many practical systems, especially in the networked control systems and many industrial processes which also includes computation delay. The presence of input delays causes system instability and degrades system performance. For a nominal system with input delay, one may transform the system using a reduction method to a non-delay form and then can design a controller using techniques that are available for systems without time-delays. However, for uncertain systems, this reduction method does not transform the system into a non-time-delayed one. Due to this reason, one need to analyze such uncertain systems using analysis that are available for time-delay systems and one attempts to exploit the benefit of using the reduction method. It is studied in this work that using simple state feedback controller over the transformed model does not yield much benefit for uncertain systems. Various choices of Lyapunov-Krasovskii functional has been made to verify stability of the transformed system and establishing the above fact. At the end, it is observed that not using the transformation method but by using a PI-type state feedback controller for the non-transformed system does yield more benefit in controller design in the sense that the guaranteed robustness margin is improved considerably.