About modification of one dynamic algorithm guaranteeing the restoration of control in a dynamic system with singular matrix

The paper deals with the properties of one method of dynamic regularization for the problem of restoration of control in a dynamic system, nonlinear in time and state and linear in control. The asymptotic estimation of accuracy has been obtained for the case where the matrix of factors at control has a constant image. The possibility of obtaining guaranteed estimations is considered for the case where the change in the image of a matrix of factors is not accompanied by tending to zero of its minimal nonzero singular value.