l/sub /spl infin// problem for finite-word-length controller design

A l/sub /spl infin// control problem is formulated for digital finite-word-length (FWL) controllers with synchronous sampling and fixed-point arithmetic. The l/sub /spl infin// FWL controllers design problem is reduced to the problem of solving a quadratic matrix inequality (QMI) such that the closed-loop system is asymptotically stable. The approach can be generalized to deal with other problems such as H/sub /spl infin//, H/sub 2/ and LQR FWL control problem.