For the nonlinear discrete dynamical system x s Tx on bounded, closed kq 1 k and convex set D ; R n , we present several sufficient and necessary conditions under which the unique equilibrium point is globally exponentially asymptotically stable. The infimum of exponential bounds of convergent traje
Uniform asymptotic stability in nonlinear volterra discrete systems
โ Scribed by P.W. Eloe; M.N. Islam; Y.N. Raffoul
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 380 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
we employ the notion of total stability to obtain new criteria for uniform asymptotic stability of the zero solution of a nonlinear Volterra discrete system. Resolvent equation methods are employed, and a summability criterion on the resolvent kernel is obtained. Also, we obtain a new difference equation that the resolvent R(n, s) satisfies.
๐ SIMILAR VOLUMES
This paper studies impulsive discrete systems with time delay. Some novel criteria on uniform asymptotic stability are established by using the method of Lyapunov functions and the Razumikhin-type technique. Examples are presented to illustrate the criteria.