Flatness and quasi-static state feedback in non-linear delay systems

Abstract

Two notions from the theory of non-linear systems without time delays are generalized to non-linear delay systems: flatness and quasi-static state feedback. Depending on the generality of the relations considered, flatness properties of increasing generality are obtained: flatness, δ-flatness, π-flatness, and difference-differential flatness. It is then shown that difference-differentially flat delay systems are linearizable by a certain class of “predictive” quasi-static state feedback, i.e., that they are equivalent by such feedback to a linear controllable system. The mathematical framework is difference-differential algebra.

Acknowledgements

The authors would like to thank Jan Winkler for his contributions to an informal study of the notion of difference-differential flatness and for the simulations on the reactor example.