# Lyapunov Theory for Discrete Time Systems

arXiv: https://arxiv.org/abs/1809.05289 · HTML: https://mlsanity.com/paper/1809.05289/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2018.

## Built on by (most cited first, 16 of 16)

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- [Self-supervised Deep Hyperspectral Inpainting with the Plug and Play and Deep Image Prior Models](https://mlsanity.com/paper/2501.08195/) (2025)
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- [Learnable Mixed Nash Equilibria are Collectively Rational](https://mlsanity.com/paper/2510.14907/) (2025)
- [Mean Field Reinforcement Learning](https://mlsanity.com/paper/2607.01525/) (2026)

## Abstract (arXiv)

In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory and Separation of time scales departs from those typically used in continuous time systems that are based on twice differentiable change of variables and the multiple use of the Implicit Function Theorem and Mean Value Theorem. More specifically, by constructing a suitable Lyapunov function only Lipschitz conditions are necessary. Finally, it is shown that under mild condition on the so-called "interconnection conditions" the proposed tools can guarantee semi-global exponential stability rather than the more stringent local exponential stability typically found in the literature