Multi-Predictor Based Scheme for the Stabilization of Delayed First-Order Systems

The stabilization and control of continuous linear systems with delay are significant challenges, as well as the complexity of their analysis, which offers important research opportunities. This article presents a prediction-based scheme to control a first-order system with an unstable pole and any size of time delay. Moreover, the necessary and sufficient conditions are provided to ensure the stability of the closed-loop system with static output feedback. To implement the strategy, a scheme based on an observer-predictor is developed to mitigate the impact of the delay. This method involves partitioning the time delay into a serie of sub-predictors, where each one estimates the signal with its assigned portion of the delay. This approach ensures an accurate estimation of the complete desired signal, allowing the application of a classical controller using the signal before been delayed to stabilize the system. The main contribution of this work is to establish a minimum number of sub-predictors such that the closed-loop system can be stabilized regardless of the delay size. Finally, an example with simulation is presented to illustrate the obtained results.