The steady-state response of a nonlinear control system, lyapunov stable attractors, and forced oscillations

Abstract

In this paper, we study the existence of periodic solutions to periodically forced systems in both the equilibrium and the nonequilibrium cases. In the equilibrium case, we prove an averaging theorem. Then, we develop the rigorous theory of the steady-state response of a nonlinear control system in order to derive some positive results on periodic forcing of autonomous systems with global Lyapunov attractors. Finally, on this occasion it is so much of a pleasure to thank Alberto Isidori for all he taught us and for all the joy we shared, and continue to share, in our research. Tanti auguri! © 2008 Springer-Verlag.