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Large scale systems stability under structural and singular perturbations. (English) Zbl 0649.93003

Lecture Notes in Control and Information Sciences, 92. Berlin etc.: Springer-Verlag. xvi, 366 p., DM 84.00 (1987).
[For a review of the Russian original (Naukova Dumka, Kiev 1984) see Zbl 0582.93048.]
This book contains an up-to-date presentation of Lyapunov stability theory and its applications to large scale systems under structural and singular perturbations. It consists of five chapters, each with a separate list of references.
Chapter 1 contains a general treatment of Lyapunov stability theory. After standard stability definitions and theorems, the authors study stability conditions on time-varying sets, and establish necessary and sufficient conditions for uniform absolute stability of time-varying Lur’e-Postnikov systems.
Chapter II is devoted to the stability theory of comparison systems, and to a study of the link between the stability conditions for a system and an associated comparison system. Both scalar and vector Lyapunov functions are considered.
Chapter III deals with the analysis of stability of large scale systems through a decomposition-aggregation approach. Both Bailey’s and Matrosov’s use of vector Lyapunov functions in stability analysis, and the robustness of stability properties under structural perturbations are studied in detail.
Chapter IV contains results concerning stability of singularly perturbed large scale systems, with both uniform and non-uniform time scaling.
Finally, Chapter V presents applications of the theory and results of the previous chapters to stability analysis of multimachine power systems.
Reviewer: M. Sezer

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93A15 Large-scale systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34D10 Perturbations of ordinary differential equations
34D15 Singular perturbations of ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
93B35 Sensitivity (robustness)

Citations:

Zbl 0582.93048