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The YJBK parametrization characterizes all stabilizing controllers. In industry, most controllers are PID and there is no solution to the problem: can a plant P(s) be stabilized by a PID controller? In this paper, we provide an answer to this question. Besides settling the question of existence, we provide a computationally constructive characterization of all stabilizing PID controllers that stabilize a given plant. Thus this result is essentially an extension of the YJBK characterization restricted to PIDs and opens up the possibility of optimal design using PIDs.