Transfer matrix method for deriving transfer functions of LTI systems

Abstract

This paper presents a new method, called the transfer matrix method for obtaining transfer functions among the state variables of a linear time-invariant (LTI) system defined in either a block diagram or the corresponding signal flow graph. The procedures introduced in this paper for obtaining the transfer function require only knowledge on matrix operations, which are easy to explain and remember. Advanced control engineers can automate the symbolic matrix operation by using existing software such as Mathematica.