# On the sample complexity of stabilizing linear dynamical systems from data

arXiv: https://arxiv.org/abs/2203.00474 · HTML: https://mlsanity.com/paper/2203.00474/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 70 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Convergence Rates for Learning Linear Operators from Noisy Data](https://mlsanity.com/paper/2108.12515/) (2021)
- [Extracting Sparse High-Dimensional Dynamics from Limited Data](https://mlsanity.com/paper/1707.08528/) (2017)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference](https://mlsanity.com/paper/1908.11233/) (2019)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification](https://mlsanity.com/paper/1707.04791/) (2017)
- [Data-driven Structured Realization](https://mlsanity.com/paper/1611.02072/) (2016)
- [Model-free control](https://mlsanity.com/paper/1305.7085/) (2013)
- [Robust data-driven state-feedback design](https://mlsanity.com/paper/1909.04314/) (2019)
- [Data-driven balancing of linear dynamical systems](https://mlsanity.com/paper/2104.01006/) (2021)
- [Robust output-feedback stabilization for incompressible flows using low-dimensional H∞-controllers](https://mlsanity.com/paper/2103.01608/) (2021)
- [Error bounds for port-Hamiltonian model and controller reduction based on system balancing](https://mlsanity.com/paper/2012.15266/) (2020)
- [MORLAB -- The Model Order Reduction LABoratory](https://mlsanity.com/paper/2002.12682/) (2020)

## Built on by (most cited first, 8 of 8)

- [A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems](https://mlsanity.com/paper/2410.03108/) (2024)
- [Context-aware controller inference for stabilizing dynamical systems from scarce data](https://mlsanity.com/paper/2207.11049/) (2022)
- [System stabilization with policy optimization on unstable latent manifolds](https://mlsanity.com/paper/2407.06418/) (2024)
- [Training-free score-based diffusion for parameter-dependent stochastic dynamical systems](https://mlsanity.com/paper/2602.02113/) (2026)
- [Safely Learning Dynamical Systems](https://mlsanity.com/paper/2305.12284/) (2023)
- [Identifying Unknown Stochastic Dynamics via Finite expression methods](https://mlsanity.com/paper/2504.07085/) (2025)
- [An adaptive data sampling strategy for stabilizing dynamical systems via controller inference](https://mlsanity.com/paper/2506.01816/) (2025)
- [Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systems](https://mlsanity.com/paper/2604.17213/) (2026)

## Abstract (arXiv)

Learning controllers from data for stabilizing dynamical systems typically follows a two step process of first identifying a model and then constructing a controller based on the identified model. However, learning models means identifying generic descriptions of the dynamics of systems, which can require large amounts of data and extracting information that are unnecessary for the specific task of stabilization. The contribution of this work is to show that if a linear dynamical system has dimension (McMillan degree) n, then there always exist n states from which a stabilizing feedback controller can be constructed, independent of the dimension of the representation of the observed states and the number of inputs. By building on previous work, this finding implies that any linear dynamical system can be stabilized from fewer observed states than the minimal number of states required for learning a model of the dynamics. The theoretical findings are demonstrated with numerical experiments that show the stabilization of the flow behind a cylinder from less data than necessary for learning a model.