# Partial stabilization of stochastic systems with application to rotating rigid bodies

## TL;DR

This paper develops a stochastic control approach to stabilize part of the variables in systems modeled by stochastic differential equations, with applications to rigid body stabilization.

## Contribution

It introduces sufficient conditions for asymptotic stability using a stochastic LaSalle's invariance principle and applies them to control rigid bodies with jet engines and rotors.

## Key findings

- Established stability conditions for stochastic systems.
- Designed state feedback controllers for rigid body stabilization.
- Validated control methods with practical examples.

## Abstract

This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets and has important applications in mechanics and engineering. Sufficient conditions for the asymptotic stability of an invariant set are proposed by using a stochastic version of LaSalle's invariance principle. These conditions are applied for constructing the state feedback controllers in the problem of single-axis stabilization of a rigid body. The cases of control torques generated by jet engines and rotors are considered as illustrations of the proposed control design methodology.