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

TL;DR

This paper introduces a unified interval observer synthesis method for locally Lipschitz nonlinear systems using mixed-monotone decompositions, ensuring correctness without extra constraints and providing LMI-based stabilizing gain conditions.

Contribution

It presents a novel observer design approach that guarantees correctness by construction for nonlinear systems without requiring global Lipschitz conditions.

Findings

The proposed observer is correct by construction for locally Lipschitz systems.

Sufficient LMI conditions for stabilizing observer gains are derived.

Performance comparisons show advantages over existing observers.

Abstract

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.