Sliding Mode Observers for Set-valued Lur'e Systems with Uncertainties Beyond Observational Range
In this paper, we introduce a new sliding mode observer for Lur'e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard range of observation. Traditionally, most of Luenberger-like observers and sliding mode observer have been designed o...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
08.02.2024
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Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we introduce a new sliding mode observer for Lur'e set-valued
dynamical systems, particularly addressing challenges posed by uncertainties
not within the standard range of observation. Traditionally, most of
Luenberger-like observers and sliding mode observer have been designed only for
uncertainties in the range of observation. Central to our approach is the
treatment of the uncertainty term which we decompose into two components: the
first part in the observation subspace and the second part in its complemented
subspace. We establish that when the second part converges to zero, an exact
sliding mode observer for the system can be obtained. In scenarios where this
convergence does not occur, our methodology allows for the estimation of errors
between the actual state and the observer state. This leads to a practical
interval estimation technique, valuable in situations where part of the
uncertainty lies outside the observable range. Finally, we show that our
observer is also a T- observer as well as a strong H-infinity observer. |
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DOI: | 10.48550/arxiv.2402.06139 |