Robust control of linear systems with structured real parameter uncertainties : quadratic stabilization approaches

Abstract

In this dissertation, uncertain linear systems with a class of time-varying real parameter uncertainties are considered based on the concept of quadratic stabilization, which relies on existence of a quadratic Lyapunov function. The real parameter uncertainties of interest are known as an effective way to describe the modeling error in state space. The dissertation has the focus on developing three control design methods - the robust LQR/LQG approaches, robust sliding mode control and constrained static output feedback stabilization. In the presence of structured real parameter uncertainties, the notion of strongly quadratic stability is defined, which combines the scaling idea with quadratic stability in order to reduce conservatism in assessing the stability issue. The stability concept has advantages in treating time-varying structured uncertainties and, moreover, taking robust performance into account specially in time domain. The main framework of the dissertation - strongly quadratic stability and guaranteed cost control - does systematize some of control design methods under the optimal control as addressed below. Regarding linear systems with the measurement and system noises, LQG control has been criticized due to the lack of robustness against parameter perturbations in system models. Based on strongly quadratic stability (and stabilizability), the LQR/LQG approaches can be extended to handle real parameter uncertainties. The proposed approach so-called robust LQG control seeks for an observer-based dynamic compensator with the same order of systems based on the guaranteed cost approach. While the full state feedback problem called robust LQR is completely solvable by using linear matrix inequalities (LMIs) methods, the robust LQG synthesis remains difficult to solve. To address this issue, a gradient search with the Block-Diagonal Riccati Approach is proposed. The Block-Diagonal Riccati Approach efficiently finds a quadratically stabilizing observer-...