Optimal tracking and tracking performance constraints from quantization

This paper studies the tracking performance of linear time-invariant (LTI) single-input single-output (SISO) discrete-time networked feedback systems. We take the system´s reference input as a step signal, and assume that the controller output is first quantized and next transmitted over a communication network to the plant, whereas the quantization error is modeled as a white noise. We are interested in the tracking performance of the systems, which is defined as the minimum mean square error between the reference input and the system´s output. We derive explicit expressions of the best attainable tracking performance for two typical configurations of networked feedback systems. The results provide fundamental performance bounds achievable using quantized control, demonstrating how the tracking performance may be constrained by the plant nonminimum phase zeros and the quantization precision. In addition, we present an output feedback design for a linear system with a multiplicative noise which is used to model the networked system in this work.