Signal-to-Noise Ratio Limitations in Structured Feedback Control

In this paper we address the problem of stabilization of multiple feedback control loops subject to signal-to-noise ratio (SNR) constraints. We consider in particular a two loop cascade control configuration and a coupled configuration that arises in control of water canals. In the cascade configuration we first study the presence of one communication channel, initially modeled as a memoryless additive white Gaussian noise (AWGN) channel and in a later stage as an additive colored Gaussian noise channel (ACGN) with memory. We then discuss the more challenging case of two simultaneous channels, one in the inner loop and one in the outer loop at different locations in each loop. In the water canal inspired configuration we consider n feedback loops and discuss the presence of communication channels, either memoryless AWGN channels or ACGN channels with memory, all simultaneously over the measurement path of each loop (between the plant and the controller), or over the control path of each loop (between the controller and the plant).