# Is It Possible to Stabilize Disrete-time Parameterized Uncertain Systems Growing Exponentially Fast?

arXiv: https://arxiv.org/abs/1810.08128 · HTML: https://mlsanity.com/paper/1810.08128/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2018.

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

- [A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems](https://mlsanity.com/paper/2511.17436/) (2025)

## Abstract (arXiv)

This paper derives a somewhat surprising but interesting enough result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to an intuition, it shows that the growth rate of a discrete-time stabilizable system with linear parameterization is not necessarily to be small all the time. More specifically, to achieve the stabilizability, the system function f(x)=O(|x|b) with b<4 is only required for a very tiny fraction of x in ℝ, even if it grows exponentially fast for the other x. The proportion of the mentioned set in ℝ, where the system fulfills the growth rate  O(|x|b) has also been computed, for both the stabilizable and unstabilizable cases. This proportion, as indicated herein, could be arbitrarily small, while the corresponding system is stabilizable.