This paper presents sampled-data H∞ˆž-control of linear mixed continuous-time and discrete-time systems, including a mix of continuous-time and discrete-time performance signals and disturbances. However, neither continuous-time control signals nor continuous-time measurements are included. The sampling may well be multirate, i.e. different signals may be sampled by different rates, as long as a periodic pattern is repeated over the period, consisting of a number of sampling steps. In fact, the results are applicable even to arbitrary linear time-varying systems. The sampled-data system is discretised such that the continuous-time performance is reflected in the discretised or "lifted" system. This lifted system is combined with discrete-time updates at the sampling instants to achieve the sampled-data controller. The "hold-states" case is presented as a special application, when there is also a hold circuit at the controller output. The continuous-time Riccati equations with discrete-time updates then can be replaced by one discrete-time static feedback and filter Riccati equation respectively, which also reflect the intersample behaviour. Furthermore, convergence results between the discretised Riccati solutions and the corresponding continuous-time solutions are shown, when the sampling interval decreases towards zero. Simulations are shown when the results are applied to the control of a MIMO jet-engine model.