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This paper studies the problem of stabilization with optimal performance for dissipative DIHS discrete-time impulsive hybrid systems . By using Lyapunov function method, conditions are derived under which the DIHS with zero inputs is GUAS globally uniformly asymptotically stable . These GUAS results are used to design feedback control law such that a dissipative DIHS is asymptotically stabilized and the value of a hybrid performance functional can be minimized. For the case of linear DIHS withdoi:10.1155/2010/278240 fatcat:iyhfm3jeqzenvhtnia46fxogci