On an integral variant of incremental input/output-to-state stability and its use as a notion of nonlinear detectability

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).

replaced with accepted version

References in corpus (2)

• A Lyapunov function for robust stability of moving horizon estimation
• Robust stability of moving horizon estimation for continuous-time systems

Cited by in corpus (1)

• Robust stability of moving horizon estimation for continuous-time systems