# On Second-Moment Stability of Discrete-Time Linear Systems with General Stochastic Dynamics

arXiv: https://arxiv.org/abs/1911.00308 · HTML: https://mlsanity.com/paper/1911.00308/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

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

- [On the Lipschitz Constant of Deep Networks and Double Descent](https://mlsanity.com/paper/2301.12309/) (2023)
- [On the Stability Analysis of Open Federated Learning Systems](https://mlsanity.com/paper/2209.12307/) (2022)

## Abstract (arXiv)

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics, and associated Lyapunov inequalities are derived. Any type of stochastic process can be dealt with as a special case in our framework for determining system dynamics, and our results together with assumptions (i.e., restrictions) on the process immediately lead us to stability conditions for the corresponding special stochastic systems. As a demonstration of usefulness of such a framework, three selected applications are also provided.