H infinity-optimal control of sampled-data systems is considered. The
H infinity analysis or synthesis problem requires iteration on the ach
ievable performance level gamma. For each iteration, the sampled-data
problem is reduced to an equivalent discrete-time problem. In this pap
er, a new set of formulas is obtained for the equivalent discrete-time
system; in each iteration, the formulas depend on computing only one
matrix exponential function. The formulas are applied to a design exam
ple, yielding interesting results.