Cost Evaluation of multirate LQD Control

In this paper,we consider a LQG problem subject to the stochastic multirate system. By restating the problem as a periodic LQG problem, it is pointed out that the lack of measurements and control inputs in some time instants makes the problem singular. A method of transforming the problem into a nonsingular one enables us to obtain the solution,however which gives a resulting value of the LQG cost and the setimation error dynamic different with those of the original system. As a consequence, we present a optimal value of the original cost and the estimation error covariance of the original system,which are expressed by periodic Lyapunov equation respectively. The evaluation resulte can be exploited in comparing the control system performances and specifying the sampling rates.