New directions in the method of vector Lyapunov functions
This paper initiates some directions of the method of vector Lyapunov functions which will have application to large-scale dynamic systems with overlapping decompositions. It is shown that it is possible to further reduce the requirements on the Lyapunov functions by perturbing them in an appropriate expanded version of the original state space, thereby making it possible to establish stability properties under less stringent conditions. Nonuniform stability results in terms of vector Lyapunov functions, with one set of these functions defined relative to the original system and the other set with respect to the expanded version are established.
scientific article; zbMATH DE number 635926