On the structure of digital controllers with finite word length consideration

It is well known that a stable discrete-time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller. Due to the difficulties in adopting the existing stability robustness measures, a new measure is derived, which is tractable and hence enables us to handle the digital controller structure problem easily. The optimal controller structure problem is formulated by maximizing this measure. An analytical solution is presented. An algorithm is developed for finding sparser structures.