Exponential stability of non-conformable fractional-order systems
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Nadhem Echi
und
Faouzi Omri
Abstract
Recently, the authors Guzman et al. (2018) introduced a new simple well-behaved definition of the fractional derivative called non-conformable fractional derivative. In this paper we study the exponential stability of non-conformable fractional-order systems by using the Lyapunov function and Gronwall inequality. These inequalities can be used as handy tools to research stability problems of nonlinear systems. Sufficient conditions for exponential stability are given using the Lyapunov theory. Further, deals with the state feedback stabilization problems for a family of nonlinear systems satisfying a Lipschitz continuity condition. The stability of the controller is proved by means of the new Lyapunov stability theorem given in this paper. A numerical example is given to illustrate the efficiency of the obtained result.
Acknowledgements
The authors sincerely thank the associated editor and anonymous reviewers for their constructive comments that helped to improve the quality and presentation of this paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the Laplace transform
- An uncertainty principle for the windowed Bochner–Fourier transform with the complex-valued window function
- Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces
- Polynomial convergence of iterations of certain random operators in Hilbert space
- Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator
- Almost compactness in neutrosophic topological spaces
- Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations
- On the stochastic elliptic equations involving fractional derivative
- A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers
- A brief survey on the development and applications of Goebel’s coincidence point theorem in differential and integral equations
- Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy
- On random pairwise comparisons matrices and their geometry
- Statistically convergent difference sequences of bi-complex numbers
- On some inequalities concerning polynomials with restricted zeros
- New retarded nonlinear integral inequalities of Gronwall–Bellman–Pachpatte type and their applications
- On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE
- Exponential stability of non-conformable fractional-order systems
Artikel in diesem Heft
- Frontmatter
- On the Laplace transform
- An uncertainty principle for the windowed Bochner–Fourier transform with the complex-valued window function
- Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces
- Polynomial convergence of iterations of certain random operators in Hilbert space
- Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator
- Almost compactness in neutrosophic topological spaces
- Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations
- On the stochastic elliptic equations involving fractional derivative
- A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers
- A brief survey on the development and applications of Goebel’s coincidence point theorem in differential and integral equations
- Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy
- On random pairwise comparisons matrices and their geometry
- Statistically convergent difference sequences of bi-complex numbers
- On some inequalities concerning polynomials with restricted zeros
- New retarded nonlinear integral inequalities of Gronwall–Bellman–Pachpatte type and their applications
- On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE
- Exponential stability of non-conformable fractional-order systems
