THE CONTROLLABILITY OF RLCM NETWORKS OVER F(Z) AND THEIR APPLICATIONS

Abstract

The subject of controllability and observability in dynamical systems is one of the important matters in linear system theory. The controllability and observability in linear systems over the field R of real numbers were heavily studied. If the values of resistors, capacitors, and self and mutual inductors in RLCM network are regard as independently variable parameters, the network is defined over the field F(z) of all rational functions in its physical parameters. Some concepts and results on the reducibility and separability for this network are presented; the controllability problem and application are discussed. In this paper the author will discuss the relationship between separability and reducibility of RLCM networks over F(z), the relationship between the physical structure of RLCM networks and structural controllability. The results in this paper can be used to study different kinds of linear or nonlinear electrical networks (over F(z)).