State Space Parameterization of Stabilizing Multirate Controllers for MIMO Linear Time - Invariant Plants

In this paper, a parameterization of stabilizing multirate controllers which communicate with given plant via a communication channel is proposed. The communications channel does not have any quantizer and the limitation of the communication rate of the channel is model by a projection operator which is defined with the well-known lifting operator. Explicit forms of stabilizing multirate controllers are derived by solving dual periodically weighted model-matching problems with linear periodically time-varying (LPTV) control. The causality constraint of periodic controllers is automatically satisfied without any additional requirement on direct terms of the controllers. A numerical example with 5-periodic control is also provided.