A Brief Overview on Fractional Order Systems in Control Theory

In this chapter, an overview of fractional-order systems, nonlinear systems and observer-related queries is given. To begin with, fractional-order systems are introduced, and a state of the art in relation with these systems in the control theory is given. Then, different classes of nonlinear systems are presented, with a literature survey on the observer design problem for these nonlinear systems. Next, we talk about the fault diagnosis problem in engineering, focusing on the fault estimation task. A state of the art of the fault estimation works in the literature is given. The final part of this chapter deals with the observer-based control of dynamic systems. The two main kinds of control, which are the stabilization and the model reference control, are introduced, and a literature survey is presented.