LQG OPTIMAL-CONTROL OF MULTIRATE SAMPLED-DATA SYSTEMS

This note presents an LQG control synthesis technique for multirate sampled-data systems where each input has its own frequency of updating and each output has its own frequency of measurement. The skew of the outputs-sampling mechanism renders the prediction problem singular for the lack of measures at some time instants. Then an ad-hoc prediction algorithm is derived by enlarging the dimension of the state vector to be estimated and feeding the state filter with a combination of measured outputs over a past and finite interval of time. The constraints on the inputs-updating mechanism are dealt with by inserting a dynamical system corresponding to a zero-order hold into the loop.