On an Integral Variant of Incremental Input/Output-to-State Stability and Its Use as a Notion of Nonlinear Detectability
- Resource Type
- Periodical
- Authors
- Schiller, J.D.; Muller, M.A.
- Source
- IEEE Control Systems Letters IEEE Control Syst. Lett. Control Systems Letters, IEEE. 7:2341-2346 2023
- Subject
- Robotics and Control Systems
Computing and Processing
Components, Circuits, Devices and Systems
Lyapunov methods
Observers
Asymptotic stability
Standards
Stability criteria
Robust stability
Integral equations
Incremental system properties
nonlinear systems
stability
detectability
state estimation
- Language
- ISSN
- 2475-1456
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).