# Relaxed ISS Small-Gain Theorems for Discrete-Time Systems

arXiv: https://arxiv.org/abs/1406.3224 · HTML: https://mlsanity.com/paper/1406.3224/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [Stability of Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2605.01978/) (2026)

## Abstract (arXiv)

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.