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Exponential stability of linear discrete systems with multiple delays. (English) Zbl 1417.39055
Summary: The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with multiple delays \(x \left(k + 1\right) = A x \left(k\right) + \sum_{i = 1}^s B_i x \left(k - m_i\right)\), \(k = 0,1, \ldots\), where \(s \in \mathbb{N}\), \(A\) and \(B_i\) are square matrices, and \(m_i \in \mathbb{N}\). New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.
MSC:
39A30 Stability theory for difference equations
39A06 Linear difference equations
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