Hierarchical Liapunov functions

A complex system is considered as a collection of dynamic components which may be combined in different ways to form stable subassemblies (subsystems), which may serve again as units to build still more complex stable configurations. A hierarchical Liapunov function is proposed, which can be used to determine stability of the overall system obtained by the multilevel interconnection process. Stability when established in this way is hierarchically connective. That is, if at any instant in time, the hierarchical evolution of the system is interrupted, the system can fall apart in exactly the same way it was constructed and, by re-starting the process, put together again without loss of stability. This fact may be used to explain the evolution of stable forms in natural as well as man-made systems.