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.

The closed-loop stability issue of finite word length (FWL) realizations is investigated for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floatingpoint implementation to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analysed with respect to both the mantissa and exponent bits of floating-point implementation. A computationally tractable FWL closed-loop stability measure is then defined, and the method of computing the value of this measure is given. The optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed FWL closed-loop stability measure, and a numerical optimization technique 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.