Abstract
IT IS well known [l-5] that the method of vector Lyapunov functions offers a very flexible mechanism for the qualitative study of nonlinear differential systems. This method has been particularly fruitful in the investigation of large-scale dynamical systems by the method of aggregation and decomposition [5], where the use of vector Lyapunov functions is made in a natural way. The basic advantage of the method is that it reduces the study of a given largescale system into a simpler comparison system and that each component of the vector Lyapunov function needs to satisfy less rigid requirements. It has been demonstrated quite recently [2] that using the technique of perturbing Lyapunov functions and employing a family of Lyapunov functions are helpful in discussing nonuniform properties of solutions of differential systems under weaker assumptions. In this paper, we initiate a new approach to the method of vector Lyapunov functions by combining the ideas involved in the foregoing techniques and this helps in distributing the burden between groups of components of the vector Lyapunov function and the comparison function. As a result, this approach contributes to the enrichment of the method of vector Lyapunov functions by including and improving earlier known results [2] and enhancing the applicability of the method.
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