Finite-Time Input-to-State Stability and Applications to Finite-Time Control Design

This paper extends the well-known concept, Sontag's input-to-state stability (ISS), to finite-time control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, nonsmoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.