Abstract
The performance of an output is defined as the least upper bound of the absolute value of that output, as time ranges over the real numbers and the input ranges over an appropriate function space. The paper extends previous results by introducing useful input spaces. A simple relation is found between performance, the step response and a characteristic of the input space. Useful necessary and sufficient conditions for finite performance are derived. The new results are extended to multivariable systems. The appropriateness of various conventional performance indices is assessed by considering the appropriateness of their corresponding input spaces.
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