# Set Membership identification of linear systems with guaranteed simulation accuracy

arXiv: https://arxiv.org/abs/2001.07628 · HTML: https://mlsanity.com/paper/2001.07628/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)
- [Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function](https://mlsanity.com/paper/2603.16481/) (2026)
- [Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression](https://mlsanity.com/paper/2409.08801/) (2024)
- [Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems](https://mlsanity.com/paper/2504.08484/) (2025)
- [Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noises](https://mlsanity.com/paper/2603.20819/) (2026)

## Abstract (arXiv)

The problem of model identification for linear systems is considered, using a finite set of sampled data affected by a bounded measurement noise, with unknown bound. The objective is to identify one-step-ahead models and their accuracy in terms of worst-case simulation error bounds. To do so, the Set Membership identification framework is exploited. Theoretical results are derived, allowing one to estimate the noise bound and system decay rate. Then, these quantities and the data are employed to define the Feasible Parameter Set (FPS), which contains all possible models compatible with the available information. Here, the estimated decay rate is used to refine the standard FPS formulation, by adding constraints that enforce the desired converging behavior of the models' impulse response. Moreover, guaranteed simulation error bounds for an infinite future horizon are derived, improving over recent results pertaining to finite simulation horizon only. These bounds are the basis for a result and method to guarantee asymptotic stability of the identified model. Finally, the desired one-step-ahead model is identified by means of numerical optimization, and the related simulation error bounds are evaluated. Both input-output and state-space model structures are addressed. The approach is showcased on a numerical example and on real-world experimental data of the roll rate dynamics of an autonomous glider.