Observer design for a class of transport-reaction systems: A direct Lyapunov approach

A. Schaum; J. A. Moreno; E. Fridman; J. Alvarez

doi:10.3182/20090616-3-il-2002.00049

Observer design for a class of transport-reaction systems: A direct Lyapunov approach

A. Schaum^*, J. A. Moreno, E. Fridman, J. Alvarez

^*Corresponding author for this work

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The paper considers the observer design problem for a class of scalar distributed transport-reaction systems with boundary measurements, mixed Dirichlet-Neumann boundary conditions, linear (diffusive-convective) transport and nonlinear conically bounded source. A direct Lyapunov method is developed for the exponential stability analysis of the observation error. The Lyapunov functional is chosen with a constant kernel for the small values of the so-called Peclet number (i.e. the quotient of diffusion to convection time) and with a spatialdependent kernel for high Peclet numbers. The derived Lyapunov-based stability conditions correspond to the ones based on the frequency-domain analysis. A numerical example illustrates the efficiency of the method.

Original language	English
Title of host publication	ROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings
Publisher	IFAC Secretariat
Pages	284-289
Number of pages	6
Edition	PART 1
ISBN (Print)	9783902661456
DOIs	https://doi.org/10.3182/20090616-3-il-2002.00049
State	Published - 2009

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	PART 1
Volume	6
ISSN (Print)	1474-6670

Funding

Funders	Funder number
DGAPA-UNAM	IN112207-3
Consejo Nacional de Ciencia y Tecnología

Keywords

Dissipativity
Lyapunov stability
Observer design
Transport-reaction systems

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10.3182/20090616-3-il-2002.00049

Cite this

Schaum, A., Moreno, J. A., Fridman, E., & Alvarez, J. (2009). Observer design for a class of transport-reaction systems: A direct Lyapunov approach. In ROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings (PART 1 ed., pp. 284-289). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 6, No. PART 1). IFAC Secretariat. https://doi.org/10.3182/20090616-3-il-2002.00049

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abstract = "The paper considers the observer design problem for a class of scalar distributed transport-reaction systems with boundary measurements, mixed Dirichlet-Neumann boundary conditions, linear (diffusive-convective) transport and nonlinear conically bounded source. A direct Lyapunov method is developed for the exponential stability analysis of the observation error. The Lyapunov functional is chosen with a constant kernel for the small values of the so-called Peclet number (i.e. the quotient of diffusion to convection time) and with a spatialdependent kernel for high Peclet numbers. The derived Lyapunov-based stability conditions correspond to the ones based on the frequency-domain analysis. A numerical example illustrates the efficiency of the method.",

keywords = "Dissipativity, Lyapunov stability, Observer design, Transport-reaction systems",

author = "A. Schaum and Moreno, {J. A.} and E. Fridman and J. Alvarez",

note = "Funding Information: ⋆This work has been supported by DGAPA-UNAM, project IN112207-3, and CONACyT, Mexico. A. Schaum thanks CEP-UNAM for financial support.",

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Schaum, A, Moreno, JA, Fridman, E & Alvarez, J 2009, Observer design for a class of transport-reaction systems: A direct Lyapunov approach. in ROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings. PART 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. PART 1, vol. 6, IFAC Secretariat, pp. 284-289. https://doi.org/10.3182/20090616-3-il-2002.00049

Observer design for a class of transport-reaction systems: A direct Lyapunov approach. / Schaum, A.; Moreno, J. A.; Fridman, E. et al.
ROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings. PART 1. ed. IFAC Secretariat, 2009. p. 284-289 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 6, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Schaum, A.

AU - Moreno, J. A.

AU - Fridman, E.

AU - Alvarez, J.

N1 - Funding Information: ⋆This work has been supported by DGAPA-UNAM, project IN112207-3, and CONACyT, Mexico. A. Schaum thanks CEP-UNAM for financial support.

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Observer design for a class of transport-reaction systems: A direct Lyapunov approach

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