# Stabilizability preserving quotients of non-linear systems

## TL;DR

This paper investigates how quotients of non-linear control systems can be used to infer the stabilizability of the original system, introducing a method to construct control Lyapunov functions via PDEs.

## Contribution

It introduces a novel approach to determine stabilizability of non-linear systems through quotient systems and PDE-based Lyapunov function construction.

## Key findings

- Conditions under which quotient stabilizability implies original system stabilizability
- A PDE-based method for constructing control Lyapunov functions
- Characterization of obstructions via integrability conditions

## Abstract

In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions stabilizability of the quotient is sufficient to guarantee stabilizability of the original system. We develop a novel method of constructing a control Lyapunov function for the original system from the implied Lyapunov function of the quotient system, this construction involves the solution of a system of partial differential equations. By studying the integrability conditions of this associated system of partial differential equations we are able to characterize obstructions to our proposed method of constructing control Lyapunov functions in terms of the structure of the original control system.