Performance Criteria for Control Systems†

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Abstract
The class of performance criteria-----------where E is the error, t is time and v is any positive constant, includes criteria such as integral-square-error and integral-modulus-error. If M0 is denned as -------------------then Mo is the total duration of finite error, and is often equivalent to the settling time criterion. Thus the class mo embraces and generalizes many well-known performance criteria for control systems with simple transient inputs. Another class, namely is often suitable_for control systems with random inputs, and includes criteria such as ----------M0' is defined as then Mo' equals the fractional duration of finite error, and is thus the appropriate analogue for simple random inputs of the settling time criterion for simple transient inputs.

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