Sampled-data systems with continuous-time inputs and outputs, where some state variables evolve in continuous time and others evolve in discrete time, are considered. Methods are presented for computing and optimizing the L/sub 2/-induced norm of such systems, considered as operators relating square integral signals. These worst-case analysis and design results are counterparts of the H/sub infinity /-norm analysis and synthesis for purely continuous- or discrete-time systems. The analysis shows that the L/sub 2/-induced norm of a sampled-data system is smaller than gamma if certain discrete-time descriptor systems have no eigenvalue of magnitude one, and if a certain discrete-time linear time-invariant plant depending on gamma has H/sub infinity / norm smaller than gamma . The synthesis shows that the optimal attenuation problem for a four-block continuous-time plant with a digital controller can be solved with a gamma -iteration on a certain discrete-time four-block plant which depends on gamma .<>