Stable use of all available measurements without commutative coupling

Develop a distributed observer for switching networks that exploits all available measurements, including measurements that violate the commutative coupling condition, while ensuring exponential stability.

Background

The illustrative example considers a vehicle platoon in which one agent additionally measures its velocity. Incorporating that measurement changes the corresponding unobservable subspace so that it is no longer invariant under the system matrix, violating the commutative coupling assumption. Under certain switching networks, the distributed observer then becomes unstable.

The authors note that stability can still be obtained by discarding the additional measurement, but this loses information and may reduce estimation performance, particularly in the presence of measurement noise. They explicitly leave the development of a method that uses all available measurements while preserving stability unresolved.

References

Developing a method that effectively exploits all available measurements while ensuring stability over switching networks is left as a future endeavor.

— On stability of a distributed observer over switching networks: The case of commutative coupling  (2609.26065 - Koo et al., 22 Sep 2026) in Remark \ref{rmk:discarding}, following Section 5, Illustrative Example

The results also leave several directions open. For example, how to use Wasserstein contraction results for observer design, in which case, non-synchronous noise has to be taken into consideration.

— Wasserstein Contraction of Stochastic Systems on Manifolds: A Differential Approach  (2610.03264 - Wu, 2 Oct 2026) in Conclusion