Distributed Interval Observers for Bounded-Error LTI Systems

TL;DR

This paper introduces a distributed interval observer for LTI systems that guarantees state bounds through local interactions, ensuring stability and providing a practical verification algorithm, with demonstrated effectiveness via simulations.

Contribution

It presents a novel distributed interval observer design for LTI systems that guarantees state bounds without extra assumptions and offers a tractable stability verification method.

Findings

Guarantees true state bounds without additional constraints

Provides necessary and sufficient stability conditions

Demonstrates effectiveness through simulations

Abstract

This paper proposes a novel distributed interval observer design for linear time-invariant (LTI) discrete-time systems subject to bounded disturbances. In the proposed observer algorithm, each agent in a networked group exchanges locally-computed framers or interval-valued state estimates with neighbors, and coordinates its update via an intersection operation. We show that the proposed framers are guaranteed to bound the true state trajectory of the system by construction, i.e., without imposing any additional assumptions or constraints. Moreover, we provide necessary and sufficient conditions for the collective stability of the distributed observer, i.e., to guarantee the uniform boundedness of the observer error sequence. In particular, we show that such conditions can be tractably satisfied through a constructive and distributed approach. Moreover, we provide an algorithm to verify some structural conditions for a given system, which guarantee the existence of the proposed observer. Finally, simulation results demonstrate the effectiveness of our proposed method compared to an existing distributed observer in the literature.