Performance Limits for Feedback Control Systems

The problem of obtaining an output from a given plant or transducer which is as close as possible to some desired output is considered. The best possible performance that can be attained can be improved through the use of feedback only if the behavior of the transducer is not completely known. An uncertain transducer can be conveniently described by permitting its instantaneous impulse response to be anywhere between prescribed limits. An optimum control system for such a transducer is derived. The response includes an error component which is proportional to the transducer impulse response uncertainty area.