Interconnecting a System Having a Single Input-to-State Gain With a System Having a Region-Dependent Input-to-State Gain

Humberto Stein Shiromoto (1) , Vincent Andrieu (2) , Christophe Prieur (1)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 LAGEP - Laboratoire d'automatique et de génie des procédés

For an ISS system, by analyzing local and non-local properties, it is obtained different input-to-state gains. The interconnection of a system having two input-to-state gains with a system having a single ISS gain is analyzed. By employing the Small Gain Theorem for the local (resp. non-local) gains composition, it is concluded about the local (resp. global) stability of the origin (resp. of a compact set). Additionally, if the region of local stability of the origin strictly includes the region attraction of the compact set, then it is shown that the origin is globally asymptotically stable. An example illustrates the approach.

Domaines: Automatique / Robotique

Humberto Stein Shiromoto, Vincent Andrieu, Christophe Prieur. Interconnecting a System Having a Single Input-to-State Gain With a System Having a Region-Dependent Input-to-State Gain. CDC 2013 - 52nd IEEE Conference on Decision and Control, Dec 2013, Florence, Italy. pp.n/c. ⟨hal-00924633⟩