Performance Analysis And Control Of H_∞ For Generalized Delta Operator System

Recently, the study of the delta operator systems has drawn more and more considerable attention in the field of control theory, which can set up a bridge between continuous systems and discrete systems. The discretization method of delta operator can avoid the ill-conditioned problem caused by the conventional shift operator when fast sampling is adopted. The method of delta operator can make a discrete system model approach its corresponding continuous system model as the sampling period goes to zero.Thus, continuous system theory and discrete system theory can be treated in a unified framework as delta operator system theory.H_∞ control theory has become a kind of robust control theory with a relatively complete system, but as to the study of H_∞ control for singular delta operator systems, there is not any existing results.This thesis mainly studies the problems of H_∞ performance analysis and H_∞ control for singular systems via delta operator approach. Firstly, the problem of H_∞ performance analysis is considered for singular delta operator systems. By using linear matrix inequality, necessary and sufficient conditions are given such that a singular delta operator system is admissible and satisfies a prescribed H_∞ performance. Secondly, the problem of H_∞ control is investigated for singular delta operator systems. By means of matrix inequalities, the existence conditions and design methods of a suitable state feedback H_∞ controller and an output feedback H_∞ controller are obtained for singular delta operator systems, respectively. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed theoretical results.