Relaxed ISS Small-Gain Theorems for Discrete-Time Systems
Abstract
In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small-gain theorems rely on the construction of a dissipative finite-step ISS Lyapunov function which is introduced in this work. Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of ISS Lyapunov functions, are shown to be sufficient and necessary to conclude ISS of the overall system.
Keywords
Cite
@article{arxiv.1406.3224,
title = {Relaxed ISS Small-Gain Theorems for Discrete-Time Systems},
author = {Roman Geiselhart and Fabian R. Wirth},
journal= {arXiv preprint arXiv:1406.3224},
year = {2015}
}
Comments
input-to-state stability, Lyapunov methods, small-gain conditions, discrete-time non-linear systems, large-scale interconnections