Lyapunov criteria for robust forward completeness of distributed parameter systems

TL;DR

This paper establishes that robust forward completeness in distributed parameter systems can be characterized by the existence of a Lyapunov function with at most exponential growth along trajectories.

Contribution

It provides a Lyapunov-based criterion for robust forward completeness in distributed parameter systems, linking stability properties to Lyapunov functions.

Findings

Robust forward completeness is equivalent to a specific Lyapunov function condition.

Lyapunov functions increasing at most exponentially characterize system robustness.

The results offer a new tool for analyzing distributed parameter systems' stability.

Abstract

We show that the robust forward completeness for distributed parameter systems is equivalent to the existence of a corresponding Lyapunov function that increases at most exponentially along the trajectories.