A joint design method of interval function observer for discrete-continuous nonlinear interconnected systems

Yanxiu Sun; Ying Du; Yuping Zhang; Yanxiu Sun; Ying Du; Yuping Zhang

doi:10.3934/math.20251020

AIMS Mathematics

2025, Volume 10, Issue 10: 22958-22979. doi: 10.3934/math.20251020

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Research article

A joint design method of interval function observer for discrete-continuous nonlinear interconnected systems

1.
College of science, University of Science and Technology Liaoning, Anshan 114051, China
2.
Basic Course Department, Shenyang Institute of Technology, Fushun 113122, China
3.
College of science, Liaoning Petrochemical University, Fushun 113001, China

Received: 30 December 2024 Revised: 26 April 2025 Accepted: 16 May 2025 Published: 10 October 2025
MSC : 15A09, 93B07, 93B17, 93C10

The interval function observer designed to reconstructs only a linear function of the state variable. This specialized structure significantly reduces the order and complexity of the traditional state observer, making it particularly suitable for interval estimation of states—an increasingly prominent topic in control theory. First, unlike the interval state observer, the interval function observer is formally defined and constructed for nonlinear interconnected systems that exhibit discrete or continuous state changes over time. Second, sufficient conditions for the existence of such an observer are derived. Using the solution method for the generalized Sylvester equation, the gain matrix for nonlinear interconnected systems is calculated. The design method is further extended from simple systems to more complex interconnected systems. Finally, two models of interconnected systems are introduced, and the proposed design method is validated through two numerical examples, confirming its effectiveness and feasibility.
- nonlinear interconnected systems,
- interval function observer,
- generalized Sylvester systems,
- state variable reconstruction
Citation: Yanxiu Sun, Ying Du, Yuping Zhang. A joint design method of interval function observer for discrete-continuous nonlinear interconnected systems[J]. AIMS Mathematics, 2025, 10(10): 22958-22979. doi: 10.3934/math.20251020

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Abstract

The interval function observer designed to reconstructs only a linear function of the state variable. This specialized structure significantly reduces the order and complexity of the traditional state observer, making it particularly suitable for interval estimation of states—an increasingly prominent topic in control theory. First, unlike the interval state observer, the interval function observer is formally defined and constructed for nonlinear interconnected systems that exhibit discrete or continuous state changes over time. Second, sufficient conditions for the existence of such an observer are derived. Using the solution method for the generalized Sylvester equation, the gain matrix for nonlinear interconnected systems is calculated. The design method is further extended from simple systems to more complex interconnected systems. Finally, two models of interconnected systems are introduced, and the proposed design method is validated through two numerical examples, confirming its effectiveness and feasibility.

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