Unified Predefined-time Stability Conditions of Nonlinear Systems with Lyapunov Analysis

This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing theorems on predefined-time/finite-time stability. The findings proposed herein develop a nonsingular sliding mode control framework for an Euler-Lagrange system to analyze its stability, and its upper bound for the settling time can be arbitrarily determined a priori through predefined time constant.