# On stabilizability and exact observability of stochastic systems with their applications

arXiv: https://arxiv.org/abs/2307.08915 · HTML: https://mlsanity.com/paper/2307.08915/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2023.

## Built on by (most cited first, 5 of 5)

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- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [Model-free H∞ control of Ito stochastic system via off-policy reinforcement learning](https://mlsanity.com/paper/2403.04412/) (2024)
- [Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise](https://mlsanity.com/paper/2506.02613/) (2025)
- [Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach](https://mlsanity.com/paper/2608.05953/) (2026)

## Abstract (arXiv)

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a necessary and sufficient condition is given for stabilizability and weak stabilizability of stochastic systems, respectively. Some new concepts called unremovable spectrums, strong solutions, and weakly feedback stabilizing solutions are introduced. An unremovable spectrum theorem is given, which generalizes the corresponding theorem of deterministic systems to stochastic systems. A stochastic Popov-Belevith-Hautus (PBH) criterion for exact observability is obtained. For applications, we give a comparison theorem for generalized algebraic Riccati equations (GAREs), and two results on Lyapunov-type equations are obtained, which improve the previous works. Finally, we also discuss robust quadratic stabilization of uncertain stochastic systems, and a necessary and sufficient condition is given for quadratic stabilization via a linear matrix inequality (LMI).