Non-conservative discrete-time ISS small-gain conditions for closed sets

2016/12/12 by Navid Noroozi, Noroozi, Navid, Roman Geiselhart +7
Engineering · Computer Science · #Control and Stability of Dynamical Systems #Stability and Control of Uncertain Systems #Distributed Control Multi-Agent Systems

paper · pdf · doi:10.48550/arxiv.1612.03710

Abstract

This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure input-to-state stability (ISS) with respect to closed sets. Toward this end, we first develop a Lyapunov characterization of ωISS via finite-step ωISS Lyapunov functions. Then, we provide the small-gain conditions to guarantee ωISS of a network of systems. Finally, applications of our results to partial input-to-state stability, ISS of time-varying systems, synchronization problems, incremental stability, and distributed observers are given.

Citations

• Consensus Problems in Networks of Agents With Switching Topology and Time-Delays

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