On the status of stability of interconnected systems

In the present paper we report on the status of stability of complex dynamical systems. We consider those systems which may be viewed as an interconnection of lower order subsystems. We emphasize those types of results which are phrased in terms of the stability properties of the subsystems and in terms of the qualitative properties of the system interconnecting structure. We consider both Lyapunov stability and input-output stability results. In our presentation, we concentrate on selected sample results and we show how some of these results are related. We then use these sample results to identify modifications, extensions, generalizations, and applications. In this way, we are able to provide a reasonably good picture of the entire subject on hand.