A new simple unifying approach of finding the state equation model and its practical application

Abstract

In the control signal process theory, the state equation is an important approach for modelling, analyzing and designing a wide range of systems. Furthermore, the state equation is often the most efficient form from the standpoint of computer simulation for highly complex systems. The existing researches exploit the fact that for networks containing dependent sources, bridging elements and coupling elements, the derivation of the closed-form state equation becomes rather complicated. On the other hand, a simple and valuable unifying approach of finding the state equations for complicated physical systems is successfully presented in the paper. The new unifying approach needs only the substitution theorem and the author's invented simple matrix operations. The main fascinating peculiarity of this approach is exposed in its systematic, graphic and human structure that improves the shortcomings of those traditional approaches. One comparative example is proposed to show the distinguished advantages our method offers over existing methods. In order to demonstrate the practical applicability, the paper has investigated an electronic operational-amplifier circuit that can be easily stabilized by our approach. (c) 2009 Elsevier Ltd. All rights reserved.