# On annular short-time stability conditions for generalized Persidskii systems

arXiv: https://arxiv.org/abs/2204.07628 · HTML: https://mlsanity.com/paper/2204.07628/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2022.

## Built on by (most cited first, 2 of 2)

- [ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergence](https://mlsanity.com/paper/2411.02292/) (2024)
- [Learning and Current Prediction of PMSM Drive via Differential Neural Networks](https://mlsanity.com/paper/2412.09028/) (2024)

## Abstract (arXiv)

This paper studies the trajectory behavior evaluation for generalized Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced. We propose conditions for annular short-time stability, short-time boundedness with a nonzero initial state, annular settling, and output annular settling for a class of Persidskii systems. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions.