Robust H_∞ Control For Descriptor Systems With Time-Delay And Parameters Uncertainty

Descriptor systems theory has been developed profoundly since its beginning. Recently the descriptor systems with uncertainty and time-delay have been paid special attention by the researchers, because of comprehensive practical application background. This thesis studies the problems of robust H_∞control for the descriptor systems with time-delay and uncertainty. Some new design techniques and results are proposed. The main contents are as follows:1. A delay-dependent H_∞control problem for descriptor systems with time-delay is investigated. A sufficient condition for the existence of H_∞memorial state feedback controller is presented in terms of matrix inequality such that the resulting closed-loop system is asymptotically stable and guarantees H_∞performance index. The upper bounding on the weighted cross products, which often leads to conservatism, is not required for obtained delay-dependent results, and this condition fits the general descriptor system with time-delay whether it is impulse-free or not. The comparison of numerical examples demonstrates the less conservatism.2. The problem of robust H_∞control for the time-delay descriptor systems with norm-bounded parameter uncertain is addressed. A sufficient condition for the existence of H_∞robust controller is presented in terms of matrix inequality such that the resulting close-loop system guarantees robust stable with H_∞performance for all admissible parametric uncertainties. For additive and multiplicative uncertainties, the design methods of non-fragile robust H_∞controller are proposed respectively by linear matrix inequality. The results present less conservatism since they are delay-dependent. The numerical example is provided to demonstrate the effectiveness of the proposed results.3. The H_∞guaranteed cost control problem for delay systems is studied. Firstly, the definition of H_∞guaranteed cost control is proposed. For the normal system with time-delay, a delay-dependent condition for the existence of H_∞guaranteed cost state feedback controller is presented such that the resulting closed-loop system satisfis the conditions of the definition. Furthermore, based on the result above, the memorial and non-fragile robust H_∞guaranteed cost controllers are designed respectively. The numerical examples, which are provided to compare with the performance index of H_∞and H_∞guaranteed cost control, demonstrate the effectiveness and feasibility of the proposed results.