Finite Time Estimation Through a Continuous-Discrete Observer

Frédéric Mazenc 1, 2 Saeed Ahmed 3 Michael Malisoff 4
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : We study two broad classes of nonlinear time-varying continuous time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance a↵ects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the ecacy of our methods.
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Frédéric Mazenc, Saeed Ahmed, Michael Malisoff. Finite Time Estimation Through a Continuous-Discrete Observer. International Journal of Robust and Nonlinear Control, Wiley, 2018, 28 (16), pp.4831-4849. ⟨10.1002/rnc.4286 ⟩. ⟨hal-01918275⟩

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