Robust Controller Design

Since an actual plant can not be modelled perfectly, robust controllers are needed due to the existing uncertainties. The uncertain part of the model may be non-causal if the plant has time-delays possessing time-varying uncertainties. Note that, most of the robust controller design methods are based on the ``small-gain theorem'', which assumes the causality of the connected sub-systems. Because of this, some limitations on the plant may be required to ensure the causality of the uncertain part to design a robust controller. However, such an approach results in a conservative controller. In this study, allowing non-causal uncertain parts, optimal robust controller design problem for systems with multiple time-delays possessing time-varying uncertainties is considered. The problem is difficult, since these systems are infinite-dimensional and the uncertain parts are allowed to be non-causal. Since unstable controllers are not desired in practice, however, designed optimal controllers may be unstable, stable robust controller design algorithms are also considered. As a case study, the flow control problem in data-communication systems is handled.