Stability analysis of fractional-order linear system with PID controller in the output feedback structure subject to input saturation

In this paper PID controller and fractional order linear system (FO-LTI) subject to input saturation augmented in the static output feedback structure. In fact, the control scheme is defined by solving the output feedback problem. The Lyapunov direct method for stability analysis of the fractional-order linear system subject to input saturation with 0<α<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<\alpha <1$$\end{document} is adopted. The output feedback investigated in the first step. To estimate the region of attraction based on the ellipsoid approach, a new stability condition through the saturation function is embraced. Finally, the iterative LMI structure endorsed output feedback and region of attraction enlargement, as well as the stability condition approach. In fact, the main advantage of this paper is the design of the PID controller in the static output feedback layout in the presence of the saturation function, stability condition and the expansion of the region of attraction. Some numerical examples based on certain theorems are used to illustrate the superiority and effectiveness of the proposed approach.