# Avoiding observability singularities in output feedback bilinear systems

## TL;DR

This paper addresses the challenge of observability singularities in control-affine output systems, proposing a method to perturb feedback laws to ensure persistent observability despite singular inputs.

## Contribution

It introduces a transversality-based approach to modify stabilizing feedback laws, guaranteeing observability in bilinear systems with linear output under singular conditions.

## Key findings

- Perturbations can eliminate observability singularities in bilinear systems.
- The method ensures continuous observability despite singular inputs.
- Applicable to control-affine systems with linear output.

## Abstract

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback stabilizable bilinear control systems with linear output, we use a transversality approach to provide perturbations of the stabilizing state feedback law, in order to make our system observable in any time even in the presence of singular inputs.