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Historically, power steering shudder, a vibration which occurs while steering a vehicle at low speeds, has been approached with systematic component-swapping experiments. This approach was time consuming and did not necessarily yield satisfactory results. In this paper it is shown that steering shudder can be analytically approached as a control system with a closed-loop limit cycle caused by the interaction of the chassis and the steering system. This approach provides a metric for determining a vehicle's propensity to shudder and allows quick predictions of the results of changing components. The approach is model-based, and incorporates chassis and hydraulic system components. Results obtained from the control systems analysis have been validated by a vehicle study, which showed a strong correlation between subjective evaluations and the stability metric provided by the analysis.