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Conditions are established under which polynomial system matrices over R[s, z] are strictly system equivalent over R[s, z]. A counter-example is given to a more general result.

Matrices over R[s, z] which are extensions of the usual form of state-space system matrices over R[s] are considered, the main object being to investigate under what conditions such matrices are system similar over R[z]. It is found that these conditions involve not only the concept of decoupling factors of a system matrix over R[s, z] but also the new concept of decoupling zeros of such a system matrix. The connection of these decoupling zeros for a given system matrix with the corresponding transfer-function matrix is also examined.

A new approach to the determination of the domain of attraction of ordinary differential equations is applied to power systems taking into account constant damping and no saliency, constant damping and saliency, and variable damping and saliency. The results are compared with the conventional methods and are found to give a better estimate of the stability boundary. A model which includes the effects of constant damping and the velocity governor is also studied. In this third-order system, cross-sections of the stability surface for the principal planes are given, again showing the superiority of the method.