Scalar vs. vector Lyapunov functions in stability analysis of large scale systems: Raprochement

Analysis methods of large scale systems by scalar Lyapunov functions and vector Lyapunov functions are contrasted. It is shown that for most systems considered in the literature (a) the vector Lyapunov function approach reduces to the scalar Lyapunov function approach, and (b) the scalar Lyapunov function approach, when applied to these systems, can yield less conservative results than the vector Lyapunov function approach.