# Detectability, Observability and Lyapunov-Type Theorems of Linear Discrete Time-Varying Stochastic Systems with Multiplicative Noise

arXiv: https://arxiv.org/abs/1509.04379 · HTML: https://mlsanity.com/paper/1509.04379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2015.

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

- [Decentralized Online Learning for Random Inverse Problems Over Graphs](https://mlsanity.com/paper/2303.11789/) (2023)

## Abstract (arXiv)

The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, cal K∞-exact detectability (resp. cal KWFT-exact detectability, cal KFT-exact detectability, cal KN-exact detectability) and cal K∞-exact observability (resp. cal KWFT-exact observability, cal KFT-exact observability, cal KN-exact observability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalized Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, cal KN-exact observability and cal KN-exact detectability, respectively.