# Stability results for fractional differential equations with applications to control processing

@inproceedings{Matignon1996StabilityRF, title={Stability results for fractional differential equations with applications to control processing}, author={Denis Matignon}, year={1996} }

In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external stabilities are investigated. For fractional differential systems in polynomial representation, external stability is thoroughly examined. Our main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector…

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## 1,614 Citations

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## References

SHOWING 1-10 OF 39 REFERENCES

### Some Results on Controllability and Observability of Finite-dimensional Fractional Differential Systems

- Mathematics
- 1996

In this paper, some structural results of main concern for control theory are given for nite-dimensional linear fractional diierential systems. The controllability and observability properties of…

### Mathematical Control Theory: Deterministic Finite Dimensional Systems

- Mathematics
- 1990

This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.

### The Laplace Transform Method for Linear Differential Equations of the Fractional Order

- Mathematics
- 1997

The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the…

### Fractional Integrals and Derivatives: Theory and Applications

- Mathematics
- 1993

Fractional integrals and derivatives on an interval fractional integrals and derivatives on the real axis and half-axis further properties of fractional integrals and derivatives other forms of…

### An Introduction to the Fractional Calculus and Fractional Differential Equations

- Mathematics
- 1993

Historical Survey The Modern Approach The Riemann-Liouville Fractional Integral The Riemann-Liouville Fractional Calculus Fractional Differential Equations Further Results Associated with Fractional…

### Linear systems

- MathematicsProceedings of the IEEE
- 1981

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of…

### Du formalisme de la dérivation généralisée à l'unité "outils mathématiques" du logiciel CRONE

- Philosophy
- 1993

Le theme de la these s'inscrit dans le vaste projet de recherche fonde sur l'etude de la derivation generalisee (ou non entiere complexe), sa synthese et son application dans les sciences de…

### ecomposi- tion modale fractionnaire de l' equation des on- des avec pertes viscothermiques. In Journ ees d' Etudes : les syst emes d'ordre non entier en automatique

- GdR Auto cnrs,
- 1995

### Sur la repr esentation ana- lytique d'une branche uniforme d'une fonction monog ene

- Acta Math.,
- 1904