Details
| Original language | English |
|---|---|
| Pages (from-to) | 2341 - 2346 |
| Number of pages | 6 |
| Journal | IEEE Control Systems Letters |
| Volume | 7 |
| Publication status | Published - 14 Jun 2023 |
Abstract
We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system satisfies a certain continuity assumption involving the Osgood condition. We show that the proposed i-iIOSS notion is a necessary condition for the existence of a robustly globally asymptotically stable observer mapping in a time-discounted ' L^2 -to- L^\infty ' sense. In combination, our results provide a general framework for a Lyapunov-based robust stability analysis of observers for continuous-time systems, which in particular is crucial for the use of optimization-based state estimators (such as moving horizon estimation).
Keywords
- detectability, Incremental system properties, nonlinear systems, stability, state estimation
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Engineering(all)
- Control and Systems Engineering
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In: IEEE Control Systems Letters, Vol. 7, 14.06.2023, p. 2341 - 2346.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On an integral variant of incremental input/output-to-state stability and its use as a notion of nonlinear detectability
AU - Schiller, Julian D.
AU - Müller, Matthias A.
N1 - DFG Grant 426459964
PY - 2023/6/14
Y1 - 2023/6/14
N2 - We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system satisfies a certain continuity assumption involving the Osgood condition. We show that the proposed i-iIOSS notion is a necessary condition for the existence of a robustly globally asymptotically stable observer mapping in a time-discounted ' L^2 -to- L^\infty ' sense. In combination, our results provide a general framework for a Lyapunov-based robust stability analysis of observers for continuous-time systems, which in particular is crucial for the use of optimization-based state estimators (such as moving horizon estimation).
AB - We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system satisfies a certain continuity assumption involving the Osgood condition. We show that the proposed i-iIOSS notion is a necessary condition for the existence of a robustly globally asymptotically stable observer mapping in a time-discounted ' L^2 -to- L^\infty ' sense. In combination, our results provide a general framework for a Lyapunov-based robust stability analysis of observers for continuous-time systems, which in particular is crucial for the use of optimization-based state estimators (such as moving horizon estimation).
KW - detectability
KW - Incremental system properties
KW - nonlinear systems
KW - stability
KW - state estimation
UR - http://www.scopus.com/inward/record.url?scp=85162682804&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2305.05442
DO - 10.48550/arXiv.2305.05442
M3 - Article
VL - 7
SP - 2341
EP - 2346
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -