When a controller is implemented by a digital computer with A/D and D/A conversion, numerical errors can severely affect the performance of the control system. There exist realizations of a given controller transfer function exhibiting arbitrarily large effects from computational errors. Assuming sufficient excitation of the system, the problem of designing an optimal controller in the presence of both external disturbances and internal roundoff errors is solved. The results reduce to the standard LQG controller when infinite-precision computation is used. For finite precision, however, the separation principle does not hold. A penalty is also added to the cost function to penalize the sum of the wordlengths used to compute the fractional part of each state variable of the controller. This sum can be used to represent the lower bound on computer memory needed for controller synthesis. It measures controller complexity and is minimized (penalized) here.
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