Finite-Time Input-to-State Stability and Related Lyapunov Analysis

Due to the need in studying finite-time control problems, this paper extends the well-known concept, input-to-state stability (ISS). A new concept, called finite-time input-to-state stability (finite-time ISS), is proposed and is applied to the finite-time stability analysis of some nonlinear systems and the design of finite-time stabilizing feedback laws. In addressing finite-time stability and control, nonsmoothness occurs in system nonlinearities and controller functions, and poses a serious technical difficulty. It is found that finite-time ISS plays an important role in nonsmooth control, in the same way as the conventional ISS in the asymptotic stability analysis and stabilization.