Affiliation:
1. Department of Mathematics , Faculty of Sciences of Gafsa , University of Gafsa , Sidi Ahmed Zarroug, 2112 Gafsa , Tunisia
Abstract
Abstract
In this paper, we introduce a new type of stability for nonlinear impulsive systems of differential equations, namely practical h-stability. By using
the Lyapunov stability theory, some sufficient conditions which guarantee practical h-stability are established. Our original results generalize well-known fundamental stability results, practical stability, practical exponential stability and practical asymptotic stability for nonlinear time-varying impulsive systems. Then two classes of nonlinear impulsive systems, namely perturbed and cascaded impulsive systems, are discussed. Furthermore, the problem of practical h-stabilization for certain classes of nonlinear impulsive systems is considered. Finally, two numerical examples are given to show the effectiveness of our theoretical results.
Reference33 articles.
1. D. D. Bainov, A. B. Dishliev and I. M. Stamova,
Practical stability of the solutions of impulsive systems of differential-difference equations via the method of comparison and some applications to population dynamics,
ANZIAM J. 43 (2002), no. 4, 525–539.
2. D. D. Baĭnov and P. S. Simeonov,
Systems with Impulse Effect. Stability, Theory and Applications,
Ellis Horwood Ser. Math. Appl.,
Ellis Horwood, New York, 1989.
3. D. D. Baĭnov and P. S. Simeonov,
Impulsive Differential Equations. Properties of the Solutions,
Ser. Adv. Math. Appl. Sci. 28,
World Scientific, River Edge, 1995.
4. C. I. Byrnes, F. Celani and A. Isidori,
Omega-limit sets of a class of nonlinear systems that are semiglobally practically stabilized,
Internat. J. Robust Nonlinear Control 15 (2005), no. 7, 315–333.
5. T. Caraballo, M. A. Hammami and L. Mchiri,
Practical asymptotic stability of nonlinear stochastic evolution equations,
Stoch. Anal. Appl. 32 (2014), no. 1, 77–87.