The problem of digital controller structures and the effect of finite-word-length (FWL) mplementation on the closed-loop stability of digital feedback control systems is addressed. A framework is presented to derive two lower stability bounds for a closed-loop system, which are controller structure dependent and then to solve the optimal FWL controller structure problem by maximising one of these lower bonnds. This yields an improved method to design optimal finite-precision controller structures with better numerical accuracy and closed-loop stability characteristics. Comparisons using numerical examples from two digital controller structures demonstrate that the procedure proposed for the more efficient measure yields an improved finite controller realisation with combined lower bits and higher lower stability bounds.

The scalar mixed H2=l1 problem for discrete-time systems is considered. The continuity property of the optimal value with respect to changes in the l1 constraint is studied. An upper approximation method and a lower approximation method of the optimal value are given. Suboptimal values and superoptimal values of the problem can be obtained by solving a sequence of finite-dimensional quadratic programming problems.