Stabilizability of SISO control systems under constraints of channel capacities

In this paper, we deal with control systems where plants and controllers are connected with transmission channels of signals, and analyze their stabilizability under the constraints of the channel capacity. We show that this problem is resolved with a minimization problem of a kind of entropy of the related systems under some asymptotic conditions, and the stabilizability can be represented by the unstable poles and real zeros of the plants. This result corresponds to a synthesis version of Bode´s theorem and an extended version of the strong stabilizability of plants. We also show a design method of the optimal controller.