The design of synchronous-generator automatic regulating equipment by linearisation techniques is now firmly established. The paper presents an obvious extension of one method, where, by means of matrix algebra, a set of general coefficients related to the well known Heffron and Phillips constants is derived, which allows complex impedance terms to be included in the analysis. In keeping with modern practice, these constants are incorporated in equations which are formulated as sets of first-order differential equations. This form provides a basis for future applications of optimal control theory, and, in addition, may be scaled more easily in both time and amplitude for analogue-simulation studies. A detailed example of a multiloop a.v.r. connected to a 30MW machine is given for reference purposes. The matrix methods, used in conjunction with the matrix iterative techniques of load-flow analysis, extend naturally to multimachine systems, allowing the dynamic operating and stability problem to be investigated with respect to possible future multimachine co-ordinated control schemes.