Robustness Improvement by Dynamic State Feedback Stabilization

Abstract

A general perception is that dynamic state feedback controllers may have superior capabilities compared to the static feedback ones. Although, for nominal systems, such superiority does not exist, it may hold true for systems other than the nominal one. This thesis investigates such capabilities of dynamic state feedback controllers. First, the case of systems with time-invariant uncertainties is considered. It appears that only a limited number of example systems exist for which dynamic feedback controller has superior ability to improve tolerable uncertainty bounds. This thesis shows that not only the available ones but there exist a class of systems for which such improvement may occur. This claim has been verified by presenting more numerical examples in the category. Second, this thesis considers the class of systems with feedback delays, more specifically, systems having both input and output delays. The superiority of dynamic feedback controllers for such systems appears to be not investigated so far in literature. However, it is observed, for the first time, that if one considers a dynamic state feedback controller but with an artificial delay in its state then the tolerable delay margin improves considerably. The performance of such a controller is investigated thoroughly for scalar systems using a continuous pole placement technique for delay systems.