# Controller Design for Structured State-space Models via Contraction Theory

arXiv: https://arxiv.org/abs/2604.07069 · HTML: https://mlsanity.com/paper/2604.07069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 41 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [A Unified Algebraic Perspective on Lipschitz Neural Networks](https://mlsanity.com/paper/2303.03169/) (2023)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [dynoNet: a neural network architecture for learning dynamical systems](https://mlsanity.com/paper/2006.02250/) (2020)
- [On the stability properties of Gated Recurrent Units neural networks](https://mlsanity.com/paper/2011.06806/) (2020)
- [State Space Models as Foundation Models: A Control Theoretic Overview](https://mlsanity.com/paper/2403.16899/) (2024)
- [Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach](https://mlsanity.com/paper/2112.09046/) (2021)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Monotone, Bi-Lipschitz, and Polyak-Lojasiewicz Networks](https://mlsanity.com/paper/2402.01344/) (2024)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [SIMBa: System Identification Methods leveraging Backpropagation](https://mlsanity.com/paper/2311.13889/) (2023)
- [Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization](https://mlsanity.com/paper/1406.1256/) (2014)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [Structured state-space models are deep Wiener models](https://mlsanity.com/paper/2312.06211/) (2023)
- [Neural Distributed Controllers with Port-Hamiltonian Structures](https://mlsanity.com/paper/2403.17785/) (2024)
- [Neural Exponential Stabilization of Control-affine Nonlinear Systems](https://mlsanity.com/paper/2403.17793/) (2024)
- [Contracting Nonlinear Observers: Convex Optimization and Learning from Data](https://mlsanity.com/paper/1711.08135/) (2017)
- [Regional stability conditions for recurrent neural network-based control systems](https://mlsanity.com/paper/2409.15792/) (2024)
- [Local controllability does imply global controllability](https://mlsanity.com/paper/2110.06631/) (2021)
- [Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach](https://mlsanity.com/paper/2411.10096/) (2024)
- [Control Contraction Metrics, Robust Control and Observer Duality](https://mlsanity.com/paper/1403.5364/) (2014)
- [L2RU: a Structured State Space Model with prescribed L2-bound](https://mlsanity.com/paper/2503.23818/) (2025)

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

- [A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning](https://mlsanity.com/paper/2604.15238/) (2026)

## Abstract (arXiv)

This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.