# Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state

## TL;DR

This paper establishes necessary and sufficient conditions for stabilizing singular fractional order systems using observer-based and output feedback control, offering more general and efficient solutions than previous methods.

## Contribution

It introduces new necessary and sufficient conditions for stabilization of singular fractional systems with partially measurable states, especially enhancing output feedback control techniques.

## Key findings

- Derived conditions improve stabilization strategies for fractional systems.
- Output feedback control conditions are more general and efficient.
- Examples demonstrate the effectiveness of the proposed methods.

## Abstract

This paper is concerned with the stabilization problem of singular fractional order systems with order $\alpha\in(0,2)$. In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition for output feedback control is proposed by adopting matrix variable decoupling technique. The developed results are more general and efficient than the existing works, especially for the output feedback case. Finally, two illustrative examples are given to verify the effectiveness and potential of the proposed approaches.