caa a22 4500 467988951 CHVBK 20180323112539.0 cr unu---uuuuu 170328e19901201xx s 000 0 eng 10.1007/BF02551376 doi (NATIONALLICENCE)springer-10.1007/BF02551376 On periodic solutions of adaptive systems in the presence of periodic forcing terms [Elektronische Daten] [J. Pomet, J. Coron, L. Praly] We consider a discrete-time system consisting of a linear plant and a periodically forced feedback controller whose parameters are slowly adapted. Using degree theory, we give sufficient conditions for the existence of periodic solutions. Using linearization methods, we give sufficient conditions for their (in)stability provided the adaptation is slow enough. We then study when the degree theoretic conditions for the existence are satisfied byd-steps-ahead adaptive controllers in the presence of unmodeled dynamics and a persistently exciting periodic reference output. Springer-Verlag New York Inc., 1990 Adaptive control nationallicence Unmodeled dynamics nationallicence Averaging analysis nationallicence Periodic solutions nationallicence Degree theory nationallicence Pomet J. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut Coron J. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut Praly L. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut Mathematics of Control, Signals and Systems Springer-Verlag 3/4(1990-12-01), 373-399 0932-4194 3:4<373 1990 3 498 https://doi.org/10.1007/BF02551376 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02551376 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pomet J. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut NATIONALLICENCE 700 1- Coron J. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut NATIONALLICENCE 700 1- Praly L. Ecole des Mines, C.A.I. Section d'Automatique, 35 rue Saint Honoré, 77305, Fontainebleau Cédex, France aut NATIONALLICENCE 773 0- Mathematics of Control, Signals and Systems Springer-Verlag 3/4(1990-12-01), 373-399 0932-4194 3:4<373 1990 3 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer