Reconstruction of controls in exponentially stable linear systems subjected to small perturbations

The problem of the dynamical reconstruction of the variable input of an exponentially stable linear system subjected to small non-linear perturbations is considered. In the case of inaccurate observations of its phase trajectory, an algorithm for solving this problem is given, based on the method of control with a model. The algorithm is stable to data interference and computation errors. General constructions are illustrated by an example in which the problem of reconstructing the input of an oscillatory section is discussed.