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In this paper a nonlinear feedback control law will be constructed for a class of linear systems, To this end a. very particular criterion functional is introduced, involving a certain S-norm of the state ||x : ||x||s. When ||x:||s = 0, singular phenomena occur which are considered in detail. It is shown that optimal arcs may end up with a singular trajectory. This problem is considered for n -dimensional linear time-dependent systems with vector control.
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Frankena et al. (1979) studied this question.
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