On asymptotic stability in impulsive semidynamical systems

On asymptotic stability in impulsive semidynamical systems

In the present paper, we study results about asymptotic stability for semidynamical systems with impulses at variable times. By considering an impulsive semidynamical system ( X , π ; M , I ), we state conditions for a closed subset A of X to be asymptotically stable in the impulsive system. In orde...

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Bibliographic Details
Published in:Journal of dynamical and control systems Vol. 19; no. 3; pp. 359 - 380
Main Authors: Bonotto, E. M., Azevedo, K. A. G.
Format: Journal Article
Language:English
Published: Boston Springer US 01-07-2013
Subjects:
Asymptotic properties
Calculus of Variations and Optimal Control; Optimization
Control
Control systems
Dynamical Systems
Dynamical Systems and Ergodic Theory
Dynamics
Impulses
Mathematics
Mathematics and Statistics
Nonlinear dynamics
Nonlinear feedback
Stability
Systems Theory
Vibration
34A37
54H20
Attractors
impulsive systems
37B25
asymptotic stability
stability
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Summary:In the present paper, we study results about asymptotic stability for semidynamical systems with impulses at variable times. By considering an impulsive semidynamical system ( X , π ; M , I ), we state conditions for a closed subset A of X to be asymptotically stable in the impulsive system. In order to obtain the results we make use of Lyapunov functionals. In conclusion, we show that the continuous time three species prey–predator population controlled by a nonlinear feedback control input is still globally asymptotically stable if we consider such system with impulses perturbation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-013-9183-6