Domain of attraction of nonlinear discrete systems with delays. (English) Zbl 0939.39013
The problem of determining the domain of attraction of nonlinear continuous or discrete systems with delays is rather complicated and still open. This paper presents one method for domain of attraction determination, which is applied to nonlinear discrete systems with bounded delays. Using the properties of nonnegative matrices and inequality techniques the author proves a new sufficient condition for the domain of attraction of a nonlinear discrete system with delays. The nonlinearity is assumed to be bounded by a “quasi” linear form. If the bound is linear, the domain of attraction becomes the entire state space. In this case, the condition is sufficient for the global exponential stability of the system. The domains of attraction of two numerical examples are given and it is known from simulation for fixed-delay that the system with initial function in the given domain of attraction is indeed exponential stable.
Reviewer: Alexei V.Ivanov (St.Peterburg)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39A12 | Discrete version of topics in analysis |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
Keywords:
domain of stability; domain of attraction; nonlinear discrete systems; nonlinear difference equations; bounded delay; global exponential stability; numerical examplesReferences:
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