Robust H ∞ adaptive model following control for fractional-order systems with polytopic and bounded uncertainties subject to input saturation

This paper investigates a type of robust observer-based tracking control for the well-known inverted pendulum as an uncertain fractional-order system with two-norm bounded uncertainties subject to input saturation along with external disturbance that focuses on the case of a fractional-order α such that 0 < α < 1 . The main goal is to design a robust model following tracking control servomechanism by the side of stability analysis. This paper addresses the well-known quadratic Lyapunov function in addition to the Gronwall–Bellman lemma and the sector condition of the saturation function stability synthesis. This paper proposes an outstanding strategy to achieve the best model following robust observer in the cast of output-feedback control subject to input saturation in the framework of an uncertain fractional-order system based on the linear matrix inequality (LMI) solution. The LMI procedure can be used to achieve static output-feedback tracking control and observer gain. Several valuable theorems support this approach, and various simulation scenarios are available to showcase its effectiveness.