Distributed Observer for Linear Systems with Multirate Sampled Outputs Involving Multiple Delays

Laura-Adriana Galicia-Galicia, Omar Hernández-González (), Carlos Daniel Garcia-Beltran, Guillermo Valencia-Palomo and María-Eusebia Guerrero-Sánchez
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Laura-Adriana Galicia-Galicia: Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interior Internado Palmira S/N, Cuernavaca 62493, Mexico
Omar Hernández-González: Tecnológico Nacional de México, IT Hermosillo, Av. Tec. 115, Hermosillo 83170, Mexico
Carlos Daniel Garcia-Beltran: Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interior Internado Palmira S/N, Cuernavaca 62493, Mexico
Guillermo Valencia-Palomo: Tecnológico Nacional de México, IT Hermosillo, Av. Tec. 115, Hermosillo 83170, Mexico
María-Eusebia Guerrero-Sánchez: CONAHCyT-Tecnológico Nacional de México, IT Hermosillo, Av. Tec. 115, Hermosillo 83170, Mexico

Mathematics, 2024, vol. 12, issue 18, 1-21

Abstract: This paper focuses on the design of a continuous distributed observer for linear systems under multirate sampled output measurements involving multiple delays. It is mathematically proved that the continuous distributed observer can achieve estimation in a sensor network environment, where output measurements from each sensor are available at different sampling instants, whether these times are periodic or aperiodic, and despite the presence of multiple time-varying delays. Each sampled and delayed measurement represents a node of the network, necessitating a dedicated observer for each node, which has access to only part of the system’s output and communicates with its neighbors according to a given network graph. The exponential convergence of the error dynamics is ensured by Lyapunov stability analysis, which accounts for the influence of the sampled and delayed measurements at each node. To demonstrate the effectiveness of the proposed observer, simulation tests were conducted on the tracking control of chasing satellites in low Earth orbit (LEO), encompassing both small and large sampling rates and delays. The continuous distributed observer with sampled output measurements exhibited convergence in scenarios with different sampling intervals, even in the presence of time-varying delays, achieving asymptotic omniscience, as demonstrated in the convergence analysis.

Keywords: distributed observer; multiple delays; sampled output (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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