A Time-Barrier Lyapunov Condition for Predefined-Time Stability

TL;DR

This paper introduces a novel time-barrier Lyapunov condition that guarantees convergence of nonlinear systems within a user-defined deadline, fundamentally differing from existing autonomous predefined-time stability methods.

Contribution

It proposes a nonautonomous Lyapunov mechanism that intrinsically enforces convergence deadlines, establishing a new stability concept distinct from classical autonomous approaches.

Findings

Guarantees convergence before a predefined deadline

Introduces a divergence-based time-dependent barrier

Demonstrates the distinctness from classical autonomous methods

Abstract

Predefined-time stability enables convergence within a user-specified time independent of initial conditions. Existing results are predominantly based on autonomous Lyapunov inequalities, where the predefined-time is realized through integral bounds on state-dependent decay and therefore acts as an upper bound rather than a structurally enforced deadline. This paper introduces a time-barrier predefined-time stability concept in which convergence is enforced through a nonautonomous Lyapunov mechanism that intrinsically restricts the remaining available time. A sufficient Lyapunov-based condition is established, guaranteeing convergence before the predefined deadline via divergence of a time-dependent barrier. It is further shown that this mechanism cannot be reproduced by classical autonomous predefined-time stability formulations, thereby constituting a distinct stability notion. The proposed approach provides a concise and transparent means of enforcing hard convergence deadlines in nonlinear systems.