The LQG problem for multirate sampled-data systems

The LQG (linear quadratic Gaussian) control problem is formulated and solved for multivariable systems where the output variables of the plant are measured at different rates. These rates can be definitively less than the unique rate adopted for input updating. It is shown how a suitable description of both the plant and the skew sampling mechanism can be given in terms of a linear periodic system. Then the solution is worked out by solving a singular periodic prediction problem and by resorting to the separation principle