Fixed-Time Stability and Stabilization

Abstract

This chapter introduces some basic results of finite-time and fixed-time stability and stabilization. To illustrate these results, three interesting examples are first presented to give an insight into the key feature on a standard structure of finite-time and fixed-time stabilizations. Then formal definitions of finite-time and fixed-time stabilities are stated and corresponding stability theorems are established. Based on these concepts and stability theorems, two types of fixed-time stabilization control approaches, i.e., a terminal sliding mode design approach and a homogeneity and Lyapunov design approach, are provided. Note, however, that these two design approaches are only applicable for certain class of systems.