A Riccati equation (RE) based solution to the H∞ optimal control problem for mixed continuous/discrete-time systems is presented. The results unify a number of recently penetrated H∞ control problems. In the infinite-horizon case a periodic behaviour is assumed, and it is shown how the related continuous RE with jumps can be replaced by an equivalent discrete periodic RE. A related algebraic RE, which involves the system behaviour during one period, then can be formulated and solved by standard methods. Typical applications are control of continuous-time or discrete-time periodic systems, as well as multirate and sampled-data control, including mixed continuous and sampled-data measurements. © 1999 EUCA.