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Variable structure systems: Present and future. (English. Russian original) Zbl 0553.93002

Autom. Remote Control 44, 1105-1120 (1983); translation from Avtom. Telemekh. 1983, No. 9, 5-25 (1983).
This paper is more than a survey. It provides an assessment of the scientific arsenal accumulated in the context of variable structure systems (VSS) theory. Promising present and future development trends in VSS theory are the subject matter of the present article. In the first part the author traces how the main principles of VSS design have been built up, and he outlines the dominant role of sliding modes in the development of VSS theory. The second part is based on a promising decomposition principle which allows construction of sliding surfaces using low order subsystems. This concept offers invariance under disturbing signals and parameter variations of the controlled object. The possibility of invariance is outlined also for control systems without infinitely high gains or sliding modes. Finally, the use of state observers in VSS design is discussed, and it is shown that ideal sliding can be preserved in the presence of state observers.
Reviewer: D.Franke

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B50 Synthesis problems
93C10 Nonlinear systems in control theory
93C35 Multivariable systems, multidimensional control systems
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93D15 Stabilization of systems by feedback
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