Global stabilization of uncertain nonlinear systems via fractional-order PID

This work presents a method that analyzes the global stabilization of fractional-order un-certain nonlinear feedback systems classes with fractional-order proportional-integral- derivative (PID) controllers. Two theorems are provided to necessary conditions for global convergence to any desired setpoints by designing controllers. The first theorem addresses a class of second-order time-varying systems controlled by fractional-order PID controllers, which extends the main result about PID (Zhao and Guo, 2017) into fractional-order systems via different analysis methods. The second theorem investigates another class of first-order time-invariant systems regulated by fractional-order proportional-integral (PI) controllers. The method is illustrated on two feedback systems with controllers to ensure the global convergence of the feedback system to desired setpoints. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This work presents a method to analyze the global stabilization of fractional-order uncertain nonlinear feedback systems using fractional-order PID controllers. Two theorems are provided to design controllers that ensure global convergence to any desired setpoints.