# A finite-sample bound for identifying partially observed linear switched systems from a single trajectory

arXiv: https://arxiv.org/abs/2503.13766 · HTML: https://mlsanity.com/paper/2503.13766/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Single Trajectory Nonparametric Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2202.08311/) (2022)
- [Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systems](https://mlsanity.com/paper/2112.10753/) (2021)
- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNs](https://mlsanity.com/paper/2312.09793/) (2023)
- [Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching](https://mlsanity.com/paper/2203.09862/) (2022)
- [Towards Efficient Maximum Likelihood Estimation of LPV-SS Models](https://mlsanity.com/paper/1808.01633/) (2018)
- [Model Reduction by Moment Matching for Linear Switched Systems](https://mlsanity.com/paper/1403.1734/) (2014)
- [Minimal covariance realization and system identification algorithm for a class of stochastic linear switched systems with i.i.d. switching](https://mlsanity.com/paper/2403.14259/) (2024)

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

- [Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noises](https://mlsanity.com/paper/2603.20819/) (2026)

## Abstract (arXiv)

We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of the Ho-Kalman algorithm to recover the system matrices. Our bound guarantees statistical consistency under the assumption that the true system exhibits quadratic stability. The proof leverages the theory of weakly dependent processes. To the best of our knowledge, this is the first finite-sample bound for this algorithm in the single-trajectory setting.