TABLE OF CONTENTS We have considered problems of SISO continuous-time control system design with the highest derivative in feedback, in which uncertainties were caused by variations in the parameters of the model or unknown external disturbances and the degree of the plant model remained the same as in the system without uncertainties. Such uncertainties are usually called structured uncertainties [Slotine and Li (1991)]. The robustness of the output performance of the control systems with the highest derivative in feedback was discussed in the presence of bounded structured uncertainties. In particular, the design procedures for a controller of the form (4.38) for system (4.27) were given, where the bounded structured uncertainties were assigned by the conditions (4.28).
Another type of uncertainty in the model description is the so-called unstructured uncertainty. These reflect errors in the system degree (or relative degree). Taking them into account usually leads to examination of the plant model with an additional small pure time delay, as well as models in the form of regularly and/or singularly perturbed systems of differential equations.
From a practical viewpoint, it is more convenient to use some simplified (nominal) model of the system reflecting only the main qualitative and quantitative features of the system. A more detailed description leads to a change in the system order. For instance, accounting for actuator and/or sensor dynamics can lead to an increase in the system order (so-called fast unmodeled dynamics). So, the nominal model results from the premeditated neglect of small parameters in order to get a...
