Compensation of infinite-dimensional input dynamics

A wealth of knowledge and research results exist for control of systems with state delays and input delays. Problems with long input delays, for unstable plants, represent a particular challenge. In fact, they were the first challenge to be dealt with, in Otto J. M. Smith’s article (Smith, 1959), where a compensator, now known as the Smith predictor, was introduced five decades ago. The Smith predictor’s value is in its ability to compensate for a long input or output delay in set point regulation or constant disturbance rejection problems. However, its major limitation is that, when the plant is unstable, it fails to recover the stabilizing property of a nominal controller for the plant without delay. A substantial modification to the Smith predictor, which removes its limitation to stable plants was developed three decades ago in the form of finite spectrum assignment (FSA) controllers (Artstein, 1982; Kwon & Pearson, 1980; Manitius & Olbrot, 1979). More recent treatment of this subject can be found in the books (Michiels & Niculescu, 2007; Zhong, 2006a). In the FSA approach, the system