# Control Contraction Metric Synthesis for Discrete-time Nonlinear Systems

arXiv: https://arxiv.org/abs/2104.10352 · HTML: https://mlsanity.com/paper/2104.10352/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2021.

## Built on by (most cited first, 3 of 3)

- [Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems](https://mlsanity.com/paper/2504.17102/) (2025)
- [Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networks](https://mlsanity.com/paper/2105.05432/) (2021)
- [Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial](https://mlsanity.com/paper/2605.26577/) (2026)

## Abstract (arXiv)

Flexible manufacturing has been the trend in the area of the modern chemical process nowadays. One of the essential characteristics of flexible manufacturing is to track time-varying target trajectories (e.g. diversity and quantity of products). A possible tool to achieve time-varying targets is contraction theory. However, the contraction theory was developed for continuous time systems and there lacks analysis and synthesis tools for discrete-time systems. This article develops a systematic approach to discrete-time contraction analysis and control synthesis using Discrete-time Control Contraction Metrics (DCCM) which can be implemented using Sum of Square (SOS) programming. The proposed approach is demonstrated by illustrative example.