%0 Journal Article %1 10153397 %A Schiller, Julian D. %A Müller, Matthias A. %D 2023 %J IEEE Control Systems Letters %K #rank1 myown %P 2341-2346 %R 10.1109/LCSYS.2023.3286174 %T On an Integral Variant of Incremental Input/Output-to-State Stability and Its Use as a Notion of Nonlinear Detectability %V 7 %X 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- $L^$ ” 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).

@article{10153397, 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).}, added-at = {2024-02-07T09:39:10.000+0100}, author = {Schiller, Julian D. and Müller, Matthias A.}, biburl = {https://www.bibsonomy.org/bibtex/2fd93c5621d84c4d92875b0fdccd42814/matthiasmueller}, doi = {10.1109/LCSYS.2023.3286174}, interhash = {4e139c049e3f99f22594e6a7fc885e91}, intrahash = {fd93c5621d84c4d92875b0fdccd42814}, issn = {2475-1456}, journal = {IEEE Control Systems Letters}, keywords = {#rank1 myown}, pages = {2341-2346}, timestamp = {2024-02-07T09:39:10.000+0100}, title = {On an Integral Variant of Incremental Input/Output-to-State Stability and Its Use as a Notion of Nonlinear Detectability}, volume = 7, year = 2023 }