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

Abstract

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.

Figures (2)

• Figure 1: Convergence behavior of sliding surface $s$ and state $x_1$ in the Monte Carlo simulations with an increasing function $\psi_1(\nu)= {b}/({ {a+e^{-\alpha \nu^{p_1}}}})$.
• Figure 2: Convergence behavior of sliding surface $s$ and state $x_1$ in the Monte Carlo simulations with a decreasing function $\psi_1(\nu)={\bar{a}+e^{-\bar{\alpha} \nu^{ p_1}}}$.