On the Lack of Robustness of Observers for Systems with Uncertain, Unstable Dynamics

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Reza_KF_uncertain_unstable_A_ACC_2023.pdf (414.53 KB)

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https://ieeexplore.ieee.org/document/10156076

Permanent Link

https://doi.org/10.23919/ACC55779.2023.10156076
 http://hdl.handle.net/11603/28826

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UMBC Mechanical Engineering Department
UMBC Faculty Collection

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Author/Creator ORCID

https://orcid.org/0000-0002-4146-6275

Date

2023-07-03

Type of Work

conference papers and proceedings
postprints
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Citation of Original Publication

M. Kamaldar, A. Goel, S. A. U. Islam and D. S. Bernstein, "On the Lack of Robustness of Observers for Systems with Uncertain, Unstable Dynamics," 2023 American Control Conference (ACC), San Diego, CA, USA, 2023, pp. 1643-1648, doi: 10.23919/ACC55779.2023.10156076.

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© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Subjects

Abstract

We consider the robustness of state estimation for linear, time-invariant systems. Since state estimation is dual to full-state feedback, it may be expected that stability of the error dynamics depends continuously on perturbations of the dynamics matrix. This paper shows, however, that, if the system dynamics are unstable, then—regardless of how the filter gain is chosen—there always exist arbitrarily small perturbations of the system dynamics that give rise to unbounded state-estimation error. Since this phenomenon cannot occur in full-state feedback control, this result reveals a surprising break-down in the duality between estimation and control.