To expand the functional capabilities of industrial controllers for systems subject to external disturbances, developments to date are reviewed, and an approach permitting the generation of control signals on the basis of predictions is proposed and tested. The benefits of this approach are assessed. It is best used for large industrial equipment and systems in manufacturing and the oil and gas industry.

A new integral representation of the solutions of multi-term matrix equations with commuting matrices is proposed. Spectral decompositions of these solutions are derived. In the special case they coincide with the decompositions for the solutions of Krein equations obtained earlier. The results are applicable to the Sylvester and Lyapunov equations for linear and some bilinear systems. The practical significance of the obtained spectral decompositions is that they allow one to characterize the contribution of individual eigencomponents and their combinations into the asymptotic dynamics of perturbation energy in linear and some bilinear systems.

Using the modified transversal surface, we identify a dynamic relationship between the specific regional gross domestic product GDPreg/per, the amount of regional investments and the specific cost of research and development activities for an example of German States (Federal Lands). In addition, we assess the specific regional losses caused by the imperfect institutional component of the human potential of a region, which is a new result.

We derive analytic formulas for the prices of financial instruments in foreign currency within the framework of a stochastic model defined as the sum of a variance gamma and a Poisson process. We obtain our results for various types of dependencies in the model. The resulting formulas contain values of hypergeometric functions. Practical applications of our results include control over the activity of investors in financial markets.