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**Stability analysis for discrete-time switched time-delay systems.**
*(English)*
Zbl 1179.93145

Summary: The stability analysis problem is studied in this paper for a class of discrete-time switched time-delay systems. By using a newly constructed Lyapunov functional and the average dwell time scheme, a delay-dependent sufficient condition is derived for the considered system to be exponentially stable. The obtained results provide a solution to one of the basic problems in discrete-time switched time-delay systems, that is, to find a switching signal for which the switched time-delay system is exponentially stable. Two illustrative examples are given to demonstrate the effectiveness of the proposed results.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93C55 | Discrete-time control/observation systems |

### Keywords:

switched time-delay systems; discrete-time; exponential stability; delay-dependent; average dwell time
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\textit{W.-A. Zhang} and \textit{L. Yu}, Automatica 45, No. 10, 2265--2271 (2009; Zbl 1179.93145)

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