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, Vol. 33, No. 4: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Computer Science
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 0932-4194
• Language: English