Dissipative interval observer design for discrete‐time nonlinear systems

This paper studies the problem of designing interval observers for a family of discrete‐time nonlinear systems subject to parametric uncertainties and external disturbances. The design approach states that the interval observers are constituted by a couple of preserving order observers, one providin...

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Bibliographic Details
Published in:Asian journal of control Vol. 22; no. 4; pp. 1422 - 1436
Main Authors: Avilés, Jesús D., Moreno, Jaime A.
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc 01.07.2020
Subjects:
discrete‐time systems
dissipative observers
interval observers
Linear matrix inequalities
Mathematical analysis
Nonlinear systems
Observers
ISSN:1561-8625, 1934-6093
Online Access:Get full text
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Summary:This paper studies the problem of designing interval observers for a family of discrete‐time nonlinear systems subject to parametric uncertainties and external disturbances. The design approach states that the interval observers are constituted by a couple of preserving order observers, one providing an upper estimation of the state while the other provides a lower one. The design aim is to apply the cooperative and dissipative properties to the discrete‐time estimation error dynamics in order to guarantee that the upper and lower estimations are always above and below the true state trajectory for all times, while both estimations asymptotically converge towards a neighborhood of the true state values. The approach represents an extension to the original method proposed by the authors, which focuses on the continuous‐time nonlinear systems. In some situations, the design conditions can be formulated as bilinear matrix inequalities (BMIs) and/or linear matrix inequalities (LMIs). Two simulation examples are provided to show the effectiveness of the design approach.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.2079