Abstract :
A set of simultaneous first-order differential equations describing the behaviour of a simple class of linear electrical networks is derived and expressed as a partitioned matrix equation. Some basic relationships of linear feedback theory are then derived in matrix terms. These are: the interpretation of transfer functions in terms of the system characteristic matrix, the relationship between transfer functions in the presence and absence of feedback, and the extension of root locus techniques to the study of the loci of the eigenvalues of the system matrix. Attention is then drawn to a set of martix eigenvalue theorems which become available when feedback problems are formulated in this way, and an example is given of their use.
