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Stability and exponential stability of linear discrete systems with constant coefficients and single delay. (English) Zbl 1410.39027

Summary: This paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay \[ x(k + 1) = A x(k) + B x(k - m),\quad k = 0, 1, \ldots \] where \( A, B\) are square constant matrices and \(m \in \mathbb{N}\). Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.

MSC:

39A30 Stability theory for difference equations
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