On the attractivity of imbedded systems

A new approach designed to aid in the construction of Liapunov functions is proposed. It is based on the notion of partial properties. A given dynamic system is imbedded into an augmented system whose attractivity with respect to a part of variables is deduced by means of an auxiliary function. This leads to an exact procedure for computation of attractivity region estimates for dynamic systems. An important feature of the method is the great reduction of conservativeness of the region estimate in the case of the overlapping decomposition of large-scale systems. When applied to a multimachine power system with non-uniform damping and transfer conductances, the method gives an enlarged estimate of the region of transient stability.