Chapter Two - Stabilization techniques for large input-delay systems with uncertainty

Abstract

In this chapter, we suggest a chain of asymptotic predictors to stabilize input time delay with a large delay. The stabilization of input time-delay systems depends on a reliable predictor to design a controller without any lag. However, the well-known model-based predictors are very sensitive to the model uncertainty, which is a serious issue when the system is unstable and the time delay is large. Although the asymptotical predictors are more robust to uncertainties, the maximum delay that can be predicted is bounded. To overcome this challenge, sequential (chain) asymptotic predictors are employed to forecast the state of the system along with a large time delay. Each predictor is responsible for predicting one small portion of the delay such that the predictors collectively predict the states for a long time delay. Then we design a classical state feedback using the predicted state. We present several examples to illustrate the capability of this method to stabilize input time-delay systems.