# Risk-Aware Stability of Discrete-Time Systems

arXiv: https://arxiv.org/abs/2211.12416 · HTML: https://mlsanity.com/paper/2211.12416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2022.

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

- [Policy Evaluation in Distributional LQR](https://mlsanity.com/paper/2303.13657/) (2023)

## Abstract (arXiv)

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations research called risk functionals (i.e., risk measures) to facilitate diverse distributional characterizations. In contrast, classical stochastic stability notions characterize the state energy on average or in probability, which can obscure the variability of stochastic system behavior. After drawing connections between various risk-aware stability concepts for nonlinear systems, we specialize to linear systems and derive sufficient conditions for the satisfaction of some risk-aware stability properties. These results pertain to real-valued coherent risk functionals and a mean-conditional-variance functional. The results reveal novel noise-to-state stability properties, which assess disturbances in ways that reflect the chosen measure of risk. We illustrate the theory through examples about robustness, parameter choices, and state-feedback controllers.