Large-scale dynamic systems: Stability and structure [Book reviews

Abstract

This monograph presents the state of the art in the theory and applications of large-scale systems via the concept of vector Lyapunov functions in a very readable way and, consequently, should be of immense value to applied mathematical scientists and engineers interested in the analysis and control of complex dynamic systems. The book is written with a distinct purpose of initiating a systematic inquiry into the intricate relationship between complexity, stability, and reliability of large scale dynamic systems. The central new concept of the book is stability under structural perturbations called connecrice srabihy. The concept is of considerable practical interest since in complex processes if is common that the subsystems do not stay together for all time during operation. Furthermore, the knowledge of interconnections among the subsystems is seldom satisfactory due to model uncertainties, imprecise measurements, equipment failures, and the like. A large system is considered connectively stable if it is stable under structural perturbations whereby subsystems are disconnected from each other and again connected together during operation. This type of stability comes often for free when stability is established by vector Lyapunov functions. From the point of liew of Lyapunov theory, connective stability for large scale systems is analogous to absolute stabihty concept for Lure-Popov systems. Both concepts represent strengthenings of the standard global asymptotic stability in order to extract all that is available in the results obtained by using Lyapunov functions. It is, therefore, not surprising that for certain classes of dynamic systems it is possible to derive necessary and sufficient conditions for connective stability. An equally important aspect of the connective stability concept is the fact that stability of this type .can be established for a class of systems by showing stabihty of a single member of that class. a s fa ct may be used as a general recipe for stability analysis of systems with uncertain parameters.