Performance assessment of MIMO systems under partial information

Minimum variance (MV) can characterize the most fundamental performance limitation of a system, owing to the existence of time-delays/infinite zeros. It has been widely used as a benchmark to assess the regulatory performance of control loops. For a SISO system, this benchmark can be estimated given the information of the system time delay. In order to compute the MIMO MV benchmark, the interactor matrix associated with the plant may be needed. However, the computation of the interactor matrix requires the knowledge of Markov parameter matrices of the plant, which is rather demanding for assessment purposes only. In this paper, we propose an upper bound of the MIMO MV benchmark which can be computed with the knowledge of the interactor matrix order. If the time delays between the inputs and outputs are known, a lower bound of the MIMO MV benchmark can also be determined.