In order to make the stability analysis of dynamic systems more general and to portray natural phenomena more accurately and practically the stability analysis of the global exponential was proposed for a time-delay dynamic system with a logical selection impulse effect. The stability analysis of general impulse time-delayed dynamic systems can be extended to a certain extent. By introducing a time-delayed nonlinear dynamic system with logically selected impulsive effects the logistic functions in this dynamic system were converted into an algebraic state space representation using the half-tensor product. An impulsive Halanay differential inequality was then developed to estimate the Cauchy matrix of the linear part of the dynamic system. Based on this four assumptions were given for the vectors and functions and a basis for determining the global exponential stability of the zero solution of a nonlinear time-delayed system under the control of a logically selected pulse was obtained. The exponential convergence rate of this dynamic system was proved to be λ-η.