A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes

Abstract—A computationally tractable unified finite word length closed-loop stability measure is derived which is applicable to fixed-point, floating-point and block-floating-point representation schemes. Both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. For each arithmetic scheme, the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it. Numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes. Index Terms—Closed-loop stability, digital controller, finite word length, number representation format, optimization. I