# Stability Analysis of Monotone Systems via Max-separable Lyapunov Functions

arXiv: https://arxiv.org/abs/1607.07966 · HTML: https://mlsanity.com/paper/1607.07966/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2016.

## Built on by (most cited first, 1 of 1)

- [Monotonicity as an Architectural Bias for Robust Language Models](https://mlsanity.com/paper/2602.02686/) (2026)

## Abstract (arXiv)

We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies the existence of a max-separable Lyapunov function on a compact set; second, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and insensitivity to time-delays. This paper establishes that for monotone nonlinear systems, equivalence holds between asymptotic stability, the existence of a max-separable Lyapunov function, D-stability, and insensitivity to bounded and unbounded time-varying delays. In particular, a new and general notion of D-stability for monotone nonlinear systems is discussed and a set of necessary and sufficient conditions for delay-independent stability are derived. Examples show how the results extend the state-of-the-art.