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Exponential Stability of Impulsive Discrete Systems with Multiple Delays

The stability problem of impulsive discrete systems with multiple delays is studied. By means of the Lyapunov stability theory and discrete-time Halanay-type inequality technique, we develop sufficient conditions for the exponential stability for the impulsive discrete systems with multiple delays, which involves multiple delays not only at non-impulsive time instants but also at impulsive time instants. The results are extended to two special discrete systems: the delayed discrete systems with time delays at only impulsive time instants and the delayed discrete systems with time delays at only non-impulsive time instants. Finally, the validity of the obtained results is shown by a numerical example