Stabilizing regions of PID controller for a class of unknown nonlinear non‐affine discrete‐time systems

Abstract

Abstract Based on the technology of dynamic linearization, the stability regions of PID, PI, PD, and P type controllers are investigated for a class of unknown nonlinear non‐affine discrete‐time systems. An equivalent data model to the unknown nonlinear system is established first through the dynamic linearization technique. Then based on the established data model, the determination of the structure of PID/PI controller has been given by rigorous theoretical derivation. The closed‐loop system is shown to be asymptotically stable for the PID, PI controllers, and the output/input signals of the closed loop system are bounded for the PD and P type controllers with the method of contraction mapping principle. An example of nonlinear non‐affine discrete‐time systems is used to demonstrate its correspondingly stability regions.