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**Exponential stability criteria for discrete time-delay systems.**
*(English)*
Zbl 1312.93087

Summary: In this paper, we study the exponential stability of linear discrete time-delay systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in Hilbert spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. As an application of the main results, we discuss the exponential stability of a general nonlinear system. The main novelty of this work is that we always consider the exponential behavior of solutions with respect to an specific ball.

### MSC:

93D20 | Asymptotic stability in control theory |

93C55 | Discrete-time control/observation systems |

93C05 | Linear systems in control theory |

### Keywords:

exponential stability; discrete time systems; slowly varying coefficients; quasi-Hermitian operators
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\textit{R. Medina} and \textit{C. Martinez}, Int. J. Robust Nonlinear Control 25, No. 4, 527--541 (2015; Zbl 1312.93087)

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