Abstract
We consider an asymptotic variant of the problem of construction of the bundle of trajectories for linear system in the class of one-impulse controls with limited power resource. Suppose that discontinuous dependence for coefficients at the controls is allowed. The attraction set (AS) in the space of trajectories with the topology of pointwise convergence is constructed. The structure of the AS is determined from the solution of generalized problem in the class of finitely additive measures. The representation of the AS as attainable sets of generalized problems is obtained for the controls which correspond to application of “narrow” impulses with the total consumption of the power resource.
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