Input-to-state stability meets small-gain theory
<|reference_start|>Input-to-state stability meets small-gain theory: Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state stability as well as ISS superpositions theorems showing relations of ISS to other robust stability properties. Next, we present one of the characteristic applications of the ISS framework - the design of event-based control schemes for the stabilization of nonlinear systems. In the second half of the paper, we focus on small-gain theorems for stability analysis of finite and infinite networks with input-to-state stable components. First, we present a classical small-gain theorem in terms of trajectories for the feedback interconnection of 2 nonlinear systems. Finally, a recent Lyapunov-based small-gain result for a network with infinitely many ISS components is shown.<|reference_end|>
@article{mironchenko2024input-to-state,
    title={Input-to-state stability meets small-gain theory},
    author={Andrii Mironchenko},
    journal={arXiv preprint arXiv:2406.17909},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.17909},
    primaryClass={math.OC cs.SY eess.SY math.DS}
}