Sampled-data H∞-control for hybrid systems

We apply general results for hybrid H_∞-controller design to the sampled-data case, such that a general discrete-time problem is treated together with a continuous-time part, but there is neither continuous-time control nor continuous-time measurement. Such a sampled-data system is periodic in nature, why periodic behaviour is considered. The sampling may well be multi-rate, 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. The sampled-data system is discretised such that the continuous-time performance is reflected in the discretised or "lifted" system. The hold-states case is presented as a special case, when there is a hold circuit at the controller output. The method is Riccati equation (RE) based, and in the hold-states case the continuous-time REs with discrete-time updates can be replaced by one discrete-time RE reflecting also the continuous-time behaviour during the sampling period. The paper also presents convergence results between the discretised Riccati solutions and the corresponding continuous-time solutions, when the sampling interval decreases towards zero. Simulations are shown when the results are applied to the control of a MIMO jet-engine model.