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

摘要

For an ISS system, by analyzing local and non-local properties, it isobtained different input-to-state gains. The interconnection of a system havingtwo input-to-state gains with a system having a single ISS gain is analyzed. Byemploying the Small Gain Theorem for the local (resp. non-local) gainscomposition, it is concluded about the local (resp. global) stability of theorigin (resp. of a compact set). Additionally, if the region of local stabilityof the origin strictly includes the region attraction of the compact set, thenit is shown that the origin is globally asymptotically stable. An exampleillustrates the approach.