Optimal tracking performance with model uncertainty over a quantized control input

There has recently been significant interest in feedback control problems with communication constraints. But the existed work mainly assume that the plant has an exact model. The object of this paper is to investigate the optimal tracking problems for networked control system in the presence of plant uncertainty. This paper studies optimal tracking performance issues for finite-dimensional, continuous-time, linear time-invariant (LTI) networked control systems, in which the control input is subject to a quantization and the plant model with uncertainty. The problem under consideration amounts to determining the minimal tracking error, while we consider two-parameter controllers. The plant is assumed to be non-minimum phase and unstable, that is, the plant contains zeros in the right half and unstable poles. And we formulate the uncertainty by utilizing stochastic embedding. The integral square criterion is adopted to measure the tracking error. The results show that the quantization error and the model uncertainty, as well as the non-minimum phase zeros, can worsen the tracking performance.