# A note on approximating the nearest stable discrete-time descriptor system with fixed rank

arXiv: https://arxiv.org/abs/1807.04481 · HTML: https://mlsanity.com/paper/1807.04481/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [Learning Stable Koopman Embeddings](https://mlsanity.com/paper/2110.06509/) (2021)
- [Stable Linear Subspace Identification: A Machine Learning Approach](https://mlsanity.com/paper/2311.03197/) (2023)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)

## Abstract (arXiv)

Consider a discrete-time linear time-invariant descriptor system Ex(k+1)=Ax(k) for k ∈ mathbb Z+. In this paper, we tackle for the first time the problem of stabilizing such systems by computing a nearby regular index one stable system hat E x(k+1)= hat A x(k) with rank(hat E)=r. We reformulate this highly nonconvex problem into an equivalent optimization problem with a relatively simple feasible set onto which it is easy to project. This allows us to employ a block coordinate descent method to obtain a nearby regular index one stable system. We illustrate the effectiveness of the algorithm on several examples.