Structural Analysis of Singularly Perturbed State Models

Abstract

The paper is devoted to the analysis of a class of mathematical models containing small parameters, namely-singularly perturbed state models. These models are of special interest for the researchers, who deal with computer simulation because the models reflect distinctive properties of the object under consideration, which should be taken into account in the practical design. Specifically, under proper conditions, small variations of parameters may cause substantial changes in physical states of the actual object.Using electronic circuits as examples, structural conditions are studied, which cause the availability of singularly perturbed state models presented in the form of the set of ordinary differential equations with small parameters on derivatives of state variables. It is suggested that the proposed approach to the structural analysis of the mentioned type of mathematical models can be extended to other classes of engineering objects by invoking thewell-known principle of physical analogies.