Direct state space solution of multirate sampled-data H-2 optimal control

In serving the multirate sampled-data H-2 control problem using the lifting approach, one needs to solve a constraint discrete-time H-2 optimal control problem for a generalized plant with infinite dimensional input/output spaces. To solve this problem, the existing sampled-data H-2 design technique computes an equivalent finite dimensional discrete-time system and then designs the optimal H-2 controller for the equivalent system. In this paper, we will show that this problem can be solved using state space formulas by dealing with operators directly. The operator compositions are computed explicitly using discrete multirate lifting and matrix exponentials. The advantages of the direct method are: it is straightforward, it has clear physical meanings, and it is more efficient computationally. A sufficient condition for the existence and uniqueness of multirate sampled-data H-2 optimal controller is given in terms of the continuous-time plant. (C) 1998 Elsevier Science Ltd. All rights reserved