Opuscula Math. 41, no. 1 (2021), 145-155
Exponential stability results for variable delay difference equations
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.