A Lyapunov function for robust stability of moving horizon estimation

We provide a novel robust stability analysis for moving horizon estimation (MHE) using Lyapunov function. Additionally, we introduce linear matrix inequalities (LMIs) to verify the necessary incremental input/output-to-state ( $\boldsymbol{\delta }$ -IOSS) detectability condition. consider an MHE formulation with time-discounted quadratic objective nonlinear systems admitting exponential -IOSS show that suitable parameterization of objective, function serves as notation="LaTeX">$\boldsymbol{M}$ -step MHE. Provided is chosen large enough, this directly implies The also applicable full information estimation, where restriction exponential can be relaxed. Moreover, simple LMI conditions systematically derive functions, which allows us easily class detectable systems. This useful in context general, since most existing (robust) results depend on system being (detectable). In combination, thus framework designing schemes guaranteed stability. applicability proposed methods demonstrated chemical reactor process and 12-state quadrotor model.