Nonlinear small-gain theorems for input-to-state stability of infinite interconnections

Mironchenko, Andrii; Kawan, Christoph und Glück, Jochen (2021): Nonlinear small-gain theorems for input-to-state stability of infinite interconnections. In: Mathematics of Control Signals and Systems, Bd. 33, Nr. 4: S. 573-615

Abstract

We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain condition. We show that for finite networks of nonlinear systems this condition is equivalent to the so-called strong small-gain condition of the gain operator (and thus our results extend available results for finite networks), and for infinite networks with a linear gain operator they correspond to the condition that the spectral radius of the gain operator is less than one. We provide efficient criteria for input-to-state stability of infinite networks with linear gains, governed by linear and homogeneous gain operators, respectively.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0932-4194
• Sprache: Englisch