Conditions of Application of Distributed Systems Synthesis Methods to Multidimensional Object

The main difficulty in applying the frequency synthesis method for multidimensional lumped systems is the necessity to transform control systems to the form that allows to consider the system as a complex of independent one-dimensional lumped systems, so that the interaction between the contours could be ignored. In this work considered spatially invariant distributed object described by differential equations in partial derivatives and carried out a comparison of distributed object continuous and discrete models dynamic characteristics. The paper shows that if the discrete analogs of spatial modes are the eigenvectors of the multidimensional object transfer matrix, the object is conventionally spatially invariant and can be described by the partial differential equation. The application of this method to multidimensional systems can allow synthesizing regulators in cases where the original transfer matrix of the object is not diagonally dominant, and let to describe the laws of object dynamics more accurate.