The closed-loop stability issue of finite word length (FWL) realizations isinvestigated for digital controllers implemented in floating-point arithmetic.Unlike the existing methods which only address the effect of the mantissa bitsin floating-point implementation to the sensitivity of closed-loop stability,the sensitivity of closed-loop stability is analysed with respect to both themantissa and exponent bits of floating-point implementation. A computationallytractable FWL closed-loop stability measure is then defined, and the method ofcomputing the value of this measure is given. The optimal controller realizationproblem is posed as searching for a floating-point realization that maximizesthe proposed FWL closed-loop stability measure, and a numerical optimizationtechnique is adopted to solve for the resulting optimization problem. Simulationresults show that the proposed design procedure yields computationally efficientcontroller realizations with enhanced FWL closed-loop stability performance.
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