Multivariable multirate sampled-data systems: State-space description, transfer characteristics, and Nyquist criterion

First, a discrete-time state-space description is derived for multivariable multirate sampled-data systems. Then, the "multirate impulse modulation" (MIM) and the "symmetric-coordinate multirate impulse modulation" (SMIM) of a transfer matrix are defined and their relation to the discrete-time state-space description is clarified. Based on the above results, four stability criteria are derived. The contents of the paper will be useful to extend the modern results about continuous-time and single-rate sampled-data control systems to the multirate sampled-data case. Especially, extensions of the INA method and of the robust stability conditions will be straightforward.