Stabilization of Continuous Time Uncertain Systems with Predefined Upper Bound of Settling Time

Stability and stabilization with predefined upper bounded settling time (PUBST) for the nonlinear nonautonomous systems are studied in this paper. The concepts of input to state stability are extended to the control problems exhibiting the property of convergence with PUBST (PUBSTC). The Lyapunov functions for depicting the presence of PUBST are introduced and reffered to as PUBSTC Lyapunov functions. Furthermore, a robust sliding mode control allowing the convergence with PUBST is designed for the nonlinear systems with matched disturbances and referred to as PUBSTC-SMC. These developments are accompanied by several academic examples for better understanding.