A small-gain theorem for set stability of infinite networks: Distributed observation and ISS for time-varying networks. (September 2022)

• Record Type: Journal Article
• Authors: Noroozi, Navid; Mironchenko, Andrii; Kawan, Christoph; Zamani, Majid
• Is Part Of: European journal of control. Volume 67(2022)
• Publication Date: 2022-09
• Subjects: Interconnected systems -- Input-to-state stability -- Small-gain theorem -- Lyapunov methods; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2022.100634
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: We generalize a small-gain theorem for a network of infinitely many systems, recently developed in [Kawan et. al, IEEE TAC (2021)]. The generalized small-gain theorem addresses exponential input-to-state stability with respect to closed sets, which enables us to study diverse control-theoretic problems in a unified manner, and it also allows for agents to have infinitely many neighbors. The small-gain condition, expressed in terms of the spectral radius of a gain operator collecting all the information about the internal Lyapunov gains, has several useful characterizations which simplify the verification of the condition. To demonstrate applicability of our small-gain theorem, we apply it to the stability analysis of infinite time-varying networks as well as the design of distributed observers for infinite networks.