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On reduction theory in qualitative analysis and control of dynamic systems. (English) Zbl 1117.93024
Kleimenov, A.F. (ed.), Mathematical control theory, differential games. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica. Proc. Steklov Inst. Math. 2004, Suppl. 2, S193-S209 (2004); translation from Tr. Inst. Mat. Mekh. 10, No. 2, 20-34 (2004).
Summary: In abstract system dynamics we consider problems of preservation of dynamic properties under transition from one dynamical system to another connected with the first one by some transformations of morphism or Lyapunov function type. A suggested reduction theorem with one or other choice of objects in its formulation leads to known and new criteria of presence of dynamic properties being studied. We give examples illustrating their application and constructibility.
For the entire collection see [Zbl 1116.93012].
MSC:
93B25 Algebraic methods
93B28 Operator-theoretic methods
93D30 Lyapunov and storage functions
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