A method to evaluate the performance of dynamical systems governed by ordinary differential equations is presented. It is based on averaging functions describing system behaviour (e.g. velocities) over prescribed domains (e.g. surfaces) in phase space. Quantitative measures of motion are introduced to indicate e.g. how oscillatory or how monotone would be the response following a disturbance. Examples demonstrate how these measures serve as new design specifications whose role is to define, compare and control system performance in a more comprehensive manner. Another application of the work is to qualitative studies in both the analysis and synthesis contexts.

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