# Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systems

arXiv: https://arxiv.org/abs/2112.10753 · HTML: https://mlsanity.com/paper/2112.10753/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 52 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2002.08538/) (2020)
- [On Adaptive Linear-Quadratic Regulators](https://mlsanity.com/paper/1806.10749/) (2018)
- [Input Perturbations for Adaptive Control and Learning](https://mlsanity.com/paper/1811.04258/) (2018)
- [Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems](https://mlsanity.com/paper/2011.09929/) (2020)
- [Optimism-Based Adaptive Regulation of Linear-Quadratic Systems](https://mlsanity.com/paper/1711.07230/) (2017)
- [Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds](https://mlsanity.com/paper/2111.07018/) (2021)
- [Analysis of Stochastic Switched Systems with Application to Networked Control Under Jamming Attacks](https://mlsanity.com/paper/1704.07647/) (2017)

## Built on by (most cited first, 6 of 6)

- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [A finite-sample bound for identifying partially observed linear switched systems from a single trajectory](https://mlsanity.com/paper/2503.13766/) (2025)
- [Model-free optimal controller for discrete-time Markovian jump linear systems: A Q-learning approach](https://mlsanity.com/paper/2408.03077/) (2024)
- [Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models](https://mlsanity.com/paper/2511.03972/) (2025)
- [Learning switched non-linear dynamical systems from a single trajectory](https://mlsanity.com/paper/2607.23502/) (2026)

## Abstract (arXiv)

In this paper, we investigate the problem of system identification for autonomous Markov jump linear systems (MJS) with complete state observations. We propose switched least squares method for identification of MJS, show that this method is strongly consistent, and derive data-dependent and data-independent rates of convergence. In particular, our data-independent rate of convergence shows that, almost surely, the system identification error is Obig(√log(T)/T big) where T is the time horizon. These results show that switched least squares method for MJS has the same rate of convergence as least squares method for autonomous linear systems. We derive our results by imposing a general stability assumption on the model called stability in the average sense. We show that stability in the average sense is a weaker form of stability compared to the stability assumptions commonly imposed in the literature. We present numerical examples to illustrate the performance of the proposed method.