The Inertia Grey Modeling Theory Based on Matrix Analysis

Abstract

The inertia is an essential characteristic of an energy system. For adapting to the need of modeling for generalized energy systems such as society, economy and technology etc, the inertia grey modeling theory that has considered inertia and inspirit of the system has a significant prospect in application. In this paper, we propose a new way to set up the inertia grey modeling theory based on the matrix analysis. Sequentially, we study the expressions of the force elements of various orders in the system of matrices, and express the raw series, AGO generating series and mean generating series with force elements respectively. Meanwhile, we also obtain the mathematical structure of the force space and properties of the decomposed transformations. It is shown that the inertia grey modeling can be represented in simplified matrix forms.