ACCURATE SOLUTION ESTIMATES FOR NONLINEAR NONAUTONOMOUS VECTOR DIFFERENCE EQUATIONS

@inproceedings{RIGOBERTOMEDINAANDMIGIL2008ACCURATESE,
  title={ACCURATE SOLUTION ESTIMATES FOR NONLINEAR NONAUTONOMOUS VECTOR DIFFERENCE EQUATIONS},
  author={’ RIGOBERTOMEDINAANDM.I.GIL},
  year={2008}
}
  • ’ RIGOBERTOMEDINAANDM.I.GIL
  • Published 2008
The paper deals with the vector discrete dynamical system xk+1 = Akxk + fk(xk). The wellknown result by Perron states that this system is asymptotically stable if Ak ≡ A = const is stable and fk(x)≡ f̃ (x)= o(‖x‖). Perron’s result gives no information about the size of the region of asymptotic stability and norms of solutions. In this paper, accurate estimates for the norms of solutions are derived. They give us stability conditions for (1.1) and bounds for the region of attraction of the… CONTINUE READING

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