Time delays in large-scale systems

The paper examines classes of large scale systems problems which have been tackled by methods associated with M-matrices and vector Lyapunov functions, and shows that the insertion of time delays into the interconnection terms will preserve exponential stability, assuming that such stability is present when no time delays exist. The key is to use new types of Lyapunov-like functions for analysing the behaviour of the delay-differential equations which are encountered. These functions allow the derivation of results for time-varying systems and systems including delay functions other than a pure delay.