Cascade observer synthesis with sigmoid functions

The problems of invariant tracking problem for nonlinear under parametrical uncertainty and incomplete miserable are considered. The effective method of the synthesis of the state space observer and external and parametrical disturbances extraction is sliding mode technique. In this paper the discontinuous actions in the observer are approximated by the sigmoid actions as a limit approximation of discontinuous functions. It is shown, that approximation of sigmoid functions allows to solve the observer synthesis problem with high accuracy and possibly better in comparison with discontinuous actions.