Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 3
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

Go to article

Authors and Affiliations

Nadhem Echi
Boulbaba Ghanmi
Download PDF Download RIS Download Bibtex

Abstract

In this paper,we start by the research of the existence of Lyapunov homogeneous function for a class of homogeneous fractional Systems, then we shall prove that local and global behaviors are the same. The uniform Mittag-Leffler stability of homogeneous fractional time-varying systems is studied. A numerical example is given to illustrate the efficiency of the obtained results.
Go to article

Bibliography

[1] V. Andrieu, L. Praly, and A. Astolfi: Homogeneous approximation, recursive observer design, and output feedback. SIAM Journal on Control and Optimization, 47(4), (2008), 1814–1850, DOI: 10.1137/060675861.
[2] A. Bacciotti and L. Rosier: Liapunov Functions and Stability in Control Theory. Lecture Notes in Control and Inform. Sci, 267 (2001), DOI: 10.1007/b139028.
[3] K. Diethelm: The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Series on Complexity, Nonlinearity and Chaos, Springer, Heidelberg, 2010.
[4] M.A. Duarte-Mermoud, N. Aguila-Camacho, J.A. Gallegos, and R. Castro-Linares: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul., 22(1-3) (2015), 650–659, DOI: 10.1016/j.cnsns. 2014.10.008.
[5] H. Hermes: Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. In: Differential equations: stability and control, Proc. Int. Conf., Colorado Springs/CO (USA) 1989, Lect. Notes Pure Appl. Math. 127, 249-260 (1990).
[6] H. Hermes: Nilpotent and high-order approximations of vector field systems. SIAM Rev, 33, (1991), 238–264, DOI: 10.1137/1033050.
[7] Y. Li, Y. Chen, and I. Podlubny: Stability of fractional-order nonlinear dynamic system: Lyapunov direct method and generalized Mittag- Leffler stability. Comput. Math. Appl, 59(5) (2010), 1810–1821, DOI: 10.1016/j.camwa.2009.08.019.
[8] Y. Li, Y. Chen, and I. Podlubny: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45 (2009), 1965–1969, DOI: 10.1140/epjst/e2011-01379-1.
[9] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo: Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204 , Elsevier Science B.V., Amsterdam 2006, DOI: 10.1016/s0304- 0208(06)80001-0.
[10] T. Menard, E. Moulay, and W. Perruquetti: Homogeneous approximations and local observer design. ESAIM: Control, Optimization and Calculus of Variations, 19 (2013), 906–929, DOI: 10.1051/cocv/2012038.
[11] K.B. Oldham and J. Spanier: The Fractional Calculus. Academic Press, New-York, 1974.
[12] I. Podlubny: Fractional Differential Equations. Mathematics in Sciences and Engineering. Academic Press, San Diego, 1999.
[13] H. Rios, D. Efmov, L. Fridman, J. Moreno, and W. Perruquetti: Homogeneity based uniform stability analysis for time-varying systems. IEEE Transactions on automatic control, 61(3), (2016), 725–734, DOI: 10.1109/TAC.2015.2446371.
[14] R. Rosier: Homogeneous Lyapunov function for homogeneous continuous vector field. System & Control Letters, 19 (1992), 467–473, DOI: 10.1016/0167-6911(92)90078-7.
[15] H.T. Tuan and H. Trinh: Stability of fractional-order nonlinear systems by Lyapunov direct method. IET Control Theory Appl, 12 (2018), DOI: 10.1049/ict-cta.2018.5233.
[16] F. Zhang, C. Li, and Y.Q. Chen: Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int. J. Differ. Equ., (2011), 1–12, DOI: 10.1155/2011/635165.
Go to article

Authors and Affiliations

Tarek Fajraoui
1
Boulbaba Ghanmi
1
ORCID: ORCID
Fehmi Mabrouk
1
Faouzi Omri
1

  1. University of Gafsa, Tunisia, Faculty of Sciences of Gafsa, Department of Mathematics, University campus Sidi Ahmed Zarroug 2112 Gafsa, Tunisia
Download PDF Download RIS Download Bibtex

Abstract

In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems
Go to article

Authors and Affiliations

Sihem Boukthir
1 2
ORCID: ORCID
Boulbaba Ghanmi
3
ORCID: ORCID
Imed Basdouri
3
ORCID: ORCID
Dalil Ichalal
4
ORCID: ORCID
Jean Lerbet
5

  1. Department of Mathematics, Faculty of Sciencesof Sfax, Route Soukra Km 4, BP 802, 3018, Sfax, Tunisia
  2. The IBISC laboratory, University ofEvry Val d’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes,France
  3. Department of Mathematics, Faculty of Sciences of Gafsa, Sidi AhmedZarroug, 2112, Gafsa, Tunisia
  4. The IBISC laboratory, University of Evry Vald’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes, France
  5. The LaMME laboratory, UMR CNRS 8071, Universityof Evry Val d’Essonne, University of Paris Saclay, 23 Bd de France, 91037, Evry CEDEX, France

This page uses 'cookies'. Learn more