Trajectory based small gain theorems for parameterized systems
Romain Postoyan, Dragan Nesic
2010 AMERICAN CONTROL CONFERENCE | IEEE | Published : 2010
In this paper, trajectory based small gain theorems are developed for parameterized families of continuous-time systems. We show that the interconnection of two input-to-state stable (ISS) parameterized systems is semiglobally and practically ISS, when ISS gain functions are appropriately parameterized, and we provide explicit sufficient conditions on the parameter. A small gain theorem is also presented for the case where two parameterized systems that satisfy some input-to-state and input-to-output stability properties are interconnected with a bounded-input-bounded-state system. Obtained results are applied to several stabilization and tracking problems. © 2010 AACC.
Supported by the French Ministere de lEducation Nationale de la Recherche et de la Technologie (MENRT) and the LSS-CNRS, SUPELEC. R. Postoyan is grateful to Antoine Chaillet for helpful discussion.