Signal-to-Noise Ratio Input Constrained Control of Single-Input Multiple-Output Systems

Systems with single input and multiple outputs can be the result of output sensor redundancies and/or a spatially dependent system. In this paper we focus on a linear time invariant (LTI) single-input multiple-outputs (SIMO) system, and consider first the analysis of an SNR constrained additive white noise (AWN) channel with switched access, located between the controller(s) and the plant input. That is, a channel for which its use is switched between the multiple output feedback control loops. We then extend the study to the case of a signal-to-noise ratio (SNR) constrained transmission of the actuation signal through an AWN multiple access channel (MAC). For both channel approaches we consider first the regulation problem (with setpoint set to zero), and then include in the analysis the potential effect of a non-zero setpoint signal on the resulting SNR constraints. We conclude that, in terms of the minimal required SNR, the AWN MAC channel option is in general preferable over the switched AWN channel option if linear co-design of the encoder and decoder is available.