# Interval Observer Synthesis for Locally Lipschitz Nonlinear Dynamical Systems via Mixed-Monotone Decompositions

arXiv: https://arxiv.org/abs/2202.11689 · HTML: https://mlsanity.com/paper/2202.11689/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2022.

## Built on by (most cited first, 2 of 2)

- [Lipschitz-Regularized Critics Lead to Policy Robustness Against Transition Dynamics Uncertainty](https://mlsanity.com/paper/2404.13879/) (2024)
- [Beyond Coefficients: Forecast-Necessity Testing for Interpretable Causal Discovery in Nonlinear Time-Series Models](https://mlsanity.com/paper/2604.18751/) (2026)

## Abstract (arXiv)

This paper proposes a novel unified interval-valued observer synthesis approach for locally Lipschitz nonlinear continuous-time (CT) and discrete-time (DT) systems with nonlinear observations. A key feature of our proposed observer, which is derived using mixed-monotone decompositions, is that it is correct by construction (i.e., the true state trajectory of the system is framed by the states of the observer) without the need for imposing additional constraints and assumptions such as global Lipschitz continuity or contraction, as is done in existing approaches in the literature. Furthermore, we derive sufficient conditions for designing stabilizing observer gains in the form of Linear Matrix Inequalities (LMIs). Finally, we compare the performance of our observer design with some benchmark CT and DT observers in the literature.