Design of distributed interval observer for cyber-physical system

Danxia Li; Shan Wang; Yujie Chu; Qian Shen; Jiale Mi; Zipeng Wang; Danxia Li; Shan Wang; Yujie Chu; Qian Shen; Jiale Mi; Zipeng Wang

doi:10.3934/math.20261132

AIMS Mathematics

2026, Volume 11, Issue 9: 28436-28451. doi: 10.3934/math.20261132

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Research article Special Issues

Design of distributed interval observer for cyber-physical system

1.
School of Intelligent Engineering, Henan Institute of Technology, Xinxiang 453007, China
2.
School of Information Science and Technology, Beijing University of Technology, Beijing 100124, China

Received: 14 June 2026 Revised: 12 August 2026 Accepted: 24 August 2026 Published: 04 September 2026
MSC : 93B07, 93B53, 93C05, 93D05

Cyber-physical systems (CPS) possess the characteristics of distribution and heterogeneity. The states of each subsystem are interrelated, and the information is dispersed. A single observer can only obtain partial measurement information and is unable to estimate all the states of the system. In this paper, a distributed interval observer (DIO) design method is proposed for CPS with bounded uncertainties and affected by disturbances and noise. Compared with traditional interval observers, it no longer requires the original system to be cooperative or the estimation error system to have an order-preserving property. This broadens the application scope of distributed interval observers. Sufficient conditions for the bounded stability of the observer error system are given using Lyapunov stability theory and Riccati equation. Finally, numerical simulations prove the effectiveness of the proposed method.
- distributed interval observer,
- cyber-physical system,
- bounded uncertainty,
- state estimation
Citation: Danxia Li, Shan Wang, Yujie Chu, Qian Shen, Jiale Mi, Zipeng Wang. Design of distributed interval observer for cyber-physical system[J]. AIMS Mathematics, 2026, 11(9): 28436-28451. doi: 10.3934/math.20261132

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Abstract

Cyber-physical systems (CPS) possess the characteristics of distribution and heterogeneity. The states of each subsystem are interrelated, and the information is dispersed. A single observer can only obtain partial measurement information and is unable to estimate all the states of the system. In this paper, a distributed interval observer (DIO) design method is proposed for CPS with bounded uncertainties and affected by disturbances and noise. Compared with traditional interval observers, it no longer requires the original system to be cooperative or the estimation error system to have an order-preserving property. This broadens the application scope of distributed interval observers. Sufficient conditions for the bounded stability of the observer error system are given using Lyapunov stability theory and Riccati equation. Finally, numerical simulations prove the effectiveness of the proposed method.

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