Lotka-Volterra-like approach to large-scale systems stability

A new aggregation form of large-scale systems is proposed in this paper. It is of the ‘Lotka-Volterra’ type and appears natural for the generalized Lotka-Volterra large-scale (possibly time-varying) systems, which is shown in the paper. The Lotka-Volterra aggregation form yields a comparison system of the generalized Lotka-Volterra type, which is composed of a linear and a non-linear part. In addition this aggregation form leads to new stability conditions for time-varying large-scale systems, and enables an extension of Weissenberger's results on exponential stability domain estimates to the asymptotic stability domain estimate of time-varying systems. An advantageous feature of the system aggregation and stability analysis developed in the paper is the omission of requirements for (any particular, e.g. exponential) stability of disconnected subsystems.