# Global asymptotic stability in a perturbed higher-order linear difference equation

@inproceedings{Pituk2003GlobalAS, title={Global asymptotic stability in a perturbed higher-order linear difference equation}, author={Mih{\'a}ly Pituk}, year={2003} }

- Published 2003
DOI:10.1016/s0898-1221(03)00084-1

In this note, we give a sufficient condition for the global asymptotic stability of the zero solution of the difference equation
χ(n+1)=∑i=0kp1(n)χ(n-i)+f(n,χ(n),χ(n-1),…,χ(n-1)),n=0,1,…
where k and l are nonnegative integers, the coefficients pi(n) are real numbers, and the nonlinearity f satisfies the growth condition
|f(n,χ0,χ1,…χl|≤q0≤i≤lmax|χi|,for n = 0,1…andχiϵR0≤i≤,
where q is a constant. The stability condition is formulated in terms of the fundamental solution of the unperturbed… CONTINUE READING

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