ABSTRACT
It is well known that in the application of the Lyapunov theory to practical problems it is often difficult to find a Lyapunov function that meets all the criteria of Lyapunov theorems. The method of vector Lyapunov functions which employs several Lyapunov functions instead of one was developed in an attempt to enlarge the class of Lyapunov functions that can be used. Recently, a new direction in the method of vector Lyapunov functions was introduced. It was shown that combining the two concepts and performing the perturbation in an expanded version of the original state space enlarges the applicability of this method by further weakening the requirements on the Lyapunov functions. This new approach can be directly applied to large-scale dynamic systems with overlapping decompositions. In such systems an expansion of the original state space is performed in order to apply standard methods. The stability laws established in the expanded system are then contracted for implementation in the original system.
