Global stabilization of uncertain nonlinear systems via fractional-order PID

This work presents a method that analyzes the global stabilization of fractional-order uncertain 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.