Abstract
This paper focuses on the connection between sliding motions and low frequency modes of high-gain feedback systems in an infinite dimensional framework. We study a particular class of abstract control systems in a Hilbert space setting and analyse their high-gain behaviour through singular perturbations. We show that the "slow" motion derived from the reduced model approximates the evolution of the closed loop after a fast transient. Moreover we prove a relation between this slow component of the high-gain feedback system and sliding motions, in the spirit of the analogous result in the finite dimensional setting by Young, Kokotovic and Utkin. This paper focuses on the connection between sliding motions and low frequency modes of high-gain feedback systems in an infinite dimensional framework. We study a particular class of abstract control systems in a Hilbertspace setting and analyse their high-gain behaviour through singular perturbations. We show that the "slow" motion derived from the reduced model approximates the evolution of the closed loop after a fast transient. Moreover we prove a relation between this slow component of the high-gain feedback system and sliding motions, in the spirit of the analogous result in the finite dimensional setting by Young, Kokotovic and Utkin.