Optimal Floating-Point Realizations of Finite-Precision Digital Controllers

The paper investigates the closed-loop stability issue of finite-precision realizations for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floating-point format to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analyzed with respect to both the mantissa and exponent bits of floating-point format. A computationally tractable finite word length (FWL) closed-loop stability measure is defined, and the optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed measure. A numerical optimization approach is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance.