Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach

Authors:
Mihailo P. Lazarević;Aleksandar M. Spasić
Affiliations:
University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16 Street, 11120 Belgrade, Serbia;Institute for Technology of Nuclear and Other Mineral Raw Materials, 86 Franchet d'Esperey Street, P.O. Box 390,11000 Belgrade, Serbia
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 6
Cited 11

On linear systems with a fractional derivation: introductory theory and examples

Mathematics and Computers in Simulation - Special issue: delay systems
Time-Delay Systems: Analysis, Optimization and Applications

Time-Delay Systems: Analysis, Optimization and Applications
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Robust stability check of fractional order linear time invariant systems with interval uncertainties

Signal Processing - Fractional calculus applications in signals and systems
Technical Communique: Analytical stability bound for delayed second-order systems with repeating poles using Lambert function W

Automatica (Journal of IFAC)
Brief Analysis of fractional delay systems of retarded and neutral type

Automatica (Journal of IFAC)

Robust finite-time stability analysis of fractional order time delay systems: new results

CONTROL'10 Proceedings of the 6th WSEAS international conference on Dynamical systems and control
Integral inequalities of systems and the estimate for solutions of certain nonlinear two-dimensional fractional differential systems

Computers & Mathematics with Applications
LMI-based robust control of fractional-order uncertain linear systems

Computers & Mathematics with Applications
Some results of the degenerate fractional differential system with delay

Computers & Mathematics with Applications
Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

Computers & Mathematics with Applications
Non-Lyapunov stability and stabilization of fractional order systems including time-varying delays

Proceedings of the 15th WSEAS international conference on Systems
Fast distributed consensus seeking in large-scale sensor networks via shortcuts

International Journal of Computational Science and Engineering
Existence of solutions for fractional differential systems with antiperiodic boundary conditions

Computers & Mathematics with Applications
Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation

Automation and Remote Control
Robust asymptotical stability of fractional-order linear systems with structured perturbations

Computers & Mathematics with Applications
Non-fragile observer design for fractional-order one-sided Lipschitz nonlinear systems

International Journal of Automation and Computing

Quantified Score

Hi-index	0.98

Visualization

Abstract

In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure.