  We consider a moving horizon estimation (MHE) scheme involving a discounted
least squares objective for general nonlinear continuous-time systems. Provided
that the system is detectable (incrementally integral input/output-to-state
stable, i-iIOSS), we show that there exists a sufficiently long estimation
horizon that guarantees robust global exponential stability of the estimation
error in a time-discounted $L^2$-to-$L^\infty$ sense. In addition, we show that
i-iIOSS Lyapunov functions can be efficiently constructed by verifying certain
linear matrix inequality conditions. In combination, we propose a flexible
Lyapunov-based MHE framework in continuous time, which particularly offers more
tuning possibilities than its discrete-time analog, and provide sufficient
conditions for stability that can be easily verified in practice. Our results
are illustrated by a numerical example.
