General aggregation of large-scale systems by-vector Lyapunov functions and vector norms

Abstract

A new approach is proposed to an advantageous application of both vector Lyapunov functions and vector norms to aggregation of large-scale systems. As a result, the test of the stability property of a large-scale system is achieved without knowledge of stability properties of its subsystems. Furthermore, new completely relaxed stability conditions are established for non-stationary non-linear dynamic large-scale systems, which reduce the stability test to verification of either the Popov criterion or stability of constant matrices of order reduced to the number equal to, or possibly less than, the number of the subsystems. As by-products of the paper, linear and Aiserman conjectures are proved for classes of systems on arbitrary hierarchical level.