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In this paper, the well-posedness of direction-dependent systems is investigated. The conditions required for well-posedness are derived. When the systems are not well-posed, two possible solutions are proposed to overcome this problem. These are the inclusion of a relay-type switching and the addition of a delay. The advantages and disadvantages of each method are discussed, for various applications in modeling and control. Two practical case studies are used to show the usefulness of the results obtained.