PROJECT TITLE :

A Note on Delay Coordinates for Locally Observable Analytic Systems

ABSTRACT:

During this short note, the problem of regionally reconstructing the state of a nonlinear system is studied. To avoid computational difficulties arising in the numerical differentiation of the output, the therefore-called delay coordinates are thought-about. The assumptions of analyticity and (local) observability of the system are shown to imply that a family of mappings, induced by the delay coordinates and parameterized by a time delay parameter, provides a local diffeomorphism for generic values of such delay parameter on a sure set. A worked-out example illustrates the result.