A Robust H 2 Performance Problem forDiscrete - Time

A robust performance problem is studied for discrete-time systems with norm-bounded uncertainties. The control performance is characterized in a determin-istic setting as the average value of a quadratic cost with respect to disturbances in l 2. For linear time-invariant systems, the average cost deened in this way reduces to the H 2 norm of the system transfer function. A robust control problem is introduced by minimizing an upper bound on the worst-case performance for an uncertain plant. The control problem involves a particular mixed H 2 =H 1 problem as a subproblem. For this problem, synthesis equations in the form of coupled nonlinear matrix equations are derived, which correspond to similar equations previously obtained for the continuous-time problem.