Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method
β Scribed by M.U. Akhmetov; A. Zafer
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 117 KB
- Volume
- 248
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
The paper is concerned with the stability of the zero solution of the impulsive system
method is used as a tool in obtaining the criteria for stability, asymptotic stability, and instability of the trivial solution.
π SIMILAR VOLUMES
By means of piecewise continuous functions which are analogues of Lyapunov's functions, sufficient conditions are obtained for the existence of integral manifolds for impulsive differential-difference equations with variable impulsive perturbations.
## Abstract We will find a positive constant Ξ£~2~ such that for any 2__Ο__ βperiodic function __h__ (__t__) with zero mean value, the quadratic Newtonian equation __x__ β³ + __x__^2^ = __Ο__ + __h__ (__t__) will have exactly two 2__Ο__ βperiodic solutions with one being unstable and another being tw
In the present paper the question of the practical stability of the solutions of impulsive systems of differential-difference equations with variable impulsive perturbations is discussed. In the investigations piecewise continuous functions are used which are analogues of Lyapunov's functions, and a