Exponential Stability of Impulsive Discrete Systems with Multiple Delays

Abstract

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 exampl

Impulsive Stabilization of Dynamic Equations on Time Scales

“…It is widely known that the various types of stability of nonlinear impulsive differential equations or impulsive difference equations can be characterized by using Lyapunov's second method and inequalities [8][9][10][11]. In recent years, some authors studied the stability of impulsive dynamic systems on time scales [12][13][14][15][16].…”