caa a22 4500 467988889 CHVBK 20180323112539.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF02551370 doi (NATIONALLICENCE)springer-10.1007/BF02551370 Praly L. Section Automatique, C.A.I., Ecole des Mines, 35 Rue Saint Honore, 77305, Fontainebleau Cedex, France aut Topological orbital equivalence with asymptotic phase for a two time-scales discrete-time system [Elektronische Daten] [L. Praly] Existence, smoothness, approximation, and attractiveness of a locally integral manifold are established for a two time-scales discrete-time system. This manifold contains all the solutions remaining in a specific compact subset. It allows us to define locally a triangular system which is topologically orbitally equivalent with asymptotic phase. It follows that (in)stability properties and existence of solutions of the original system, remaining after some time instant in the above-mentioned compact subset, can be established from the study of a reduced-order system. We study this reduced-order system for a weakly nonstationary case, applying the stroboscopic method to approximate it by a practically meaningful, slowly time-varying system. Springer-Verlag New York Inc., 1990 Discrete-time system nationallicence Two time-scales system nationallicence Topological equivalence nationallicence Integral manifold nationallicence Averaging nationallicence Mathematics of Control, Signals and Systems Springer-Verlag 3/3(1990-09-01), 225-253 0932-4194 3:3<225 1990 3 498 https://doi.org/10.1007/BF02551370 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02551370 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Praly L. Section Automatique, C.A.I., Ecole des Mines, 35 Rue Saint Honore, 77305, Fontainebleau Cedex, France aut NATIONALLICENCE 773 0- Mathematics of Control, Signals and Systems Springer-Verlag 3/3(1990-09-01), 225-253 0932-4194 3:3<225 1990 3 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer