Opuscula Math. 41, no. 1 (2021), 145-155

Opuscula Mathematica

Exponential stability results for variable delay difference equations

Ernest Yankson

Abstract. Sufficient conditions that guarantee exponential decay to zero of the variable delay difference equation \[x(n+1)=a(n)x(n)+b(n)x(n-g(n))\] are obtained. These sufficient conditions are deduced via inequalities by employing Lyapunov functionals. In addition, a criterion for the instability of the zero solution is established. The results in the paper generalizes some results in the literature.

Keywords: exponential stability, Lyapunov functional, instability.

Mathematics Subject Classification: 34D20, 34D40, 34K20.

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  • Communicated by Josef Diblík.
  • Received: 2020-10-19.
  • Revised: 2020-11-13.
  • Accepted: 2020-12-14.
  • Published online: 2021-02-08.
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Cite this article as:
Ernest Yankson, Exponential stability results for variable delay difference equations, Opuscula Math. 41, no. 1 (2021), 145-155, https://doi.org/10.7494/OpMath.2021.41.1.145

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