Sampled-Data Estimator for Nonlinear Systems with Uncertainties and Arbitrarily Fast Rate of Convergence

Frédéric Mazenc (1, 2) , Michael Malisoff (3) , Silviu-Iulian Niculescu (2, 1)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 LSU Mathematics - Department of Mathematics [Baton Rouge]

We study a class of continuous-time nonlinear systems with discrete measurements, model uncertainty, and sensor noise. We provide an estimator of the state for which the observation error enjoys a variant of the exponential input-to-state stability property with respect to the model uncertainty and sensor noise. A valuable novel feature is that the overshoot term in this stability estimate only involves a recent history of uncertainty values. Also, the rate of exponential convergence can be made arbitrarily large by reducing the supremum of the sampling intervals. Our proof uses a recently developed trajectory based approach. We illustrate our work using a model for a pendulum whose suspension point is subjected to an unknown time-varying bounded horizontal oscillation.

Mots clés: Estimation; nonlinear systems; delay; stability

Domaines: Automatique

Frédéric Mazenc, Michael Malisoff, Silviu-Iulian Niculescu. Sampled-Data Estimator for Nonlinear Systems with Uncertainties and Arbitrarily Fast Rate of Convergence. Automatica, 2022, 142, pp.110361. ⟨10.1016/j.automatica.2022.110361⟩. ⟨hal-03891465⟩