On Stability Analysis of Nonlinear Systems

In this study, an extensive review of nonlinear systems and their stability analysis is given. In particular, this paper attempts to explore the differences between closed-loop and open-loop systems and demonstrates how each plays a different function in control theory. The idea of hyperbolic equilibria is investigated, along with the stable and unstable manifolds that go along with it. This exploration sheds light on the behavior of dynamical systems both locally and globally. A solid foundation for assessing the stability of nonlinear systems is provided by discussing several forms of stability, such as exponential, asymptotic, and input-to-state stability (ISS).