H_∞ Control And Filtering For Uncertain Delta Operator Systems

The control theory for pure continuous-time and discrete-time cases are pene-trated by many authors, however the distinction is frequently drawn between them.The Delta operator enables a close correspondence between discrete- and continuous-time systems theory. Thus, the study on Delta operator systems has long drawn muchattention from researchers working in control areas. Delta operator control theory hasnot formed a fairly complete framework, this prevents it from further developmentand limits its applications in practical engineering to a great extent. Establishing andperfecting robust Delta operator system are research frontiers in control area. Thisthesis, based on previous works of others, systematically and deeply investigates theproblems of H∞performance criterion, state-feedback H∞control, output-feedbackH∞control, and H∞filtering for polytopic Delta operator systems.The problem of H∞performance criterion for polytopic Delta operator systemsis investigated. From the bounded real lemma, an improved linear matrix inequalityrepresentation for H∞performance criterion is presented by introducing two slackmatrices. Utilizing the parameter-dependent idea guarantees the less conservativenessof the proposed methods gradually. To further reduce conservatism, a possible alter-native is the selection of polynomial parameter-dependent matrices. The characters ofproposed performance are systematically summarized and analyzed, on which furtherresearches are based.The state-feedback H∞control problem for polytopic Delta operator systemsis considered. According to the above mentioned H∞performance criteria, suffi-cient conditions for state-feedback H∞controller are derived in terms of matrix in-equalities. Based on the recognize of possible way to overcome the conservatism i.e.a parameter-dependent Lyapunov function method, polynomial parameter-dependentapproach is proposed. The designed H∞controllers can be obtained from the solutionof some optimization problems. The proposed controllers can guarantee the closed-loop systems to be asymptotically stable and have a prescribed H∞disturbance atten-uation performance for all admissible uncertain parameters.The problem of designing H∞dynamic output-feedback controllers for poly-topic Delta operator systems is investigated. For a given transfer function matrix of a system with polytopic uncertainty, an appropriate state-space model of the system isdescribed, which permits reconstruction of all its states. To this model, a new poly-nomial parameter-dependent approach to state-feedback H∞control is then used todesign robust output-feedback controllers, which is different from conventional de-sign framework. These controllers ensure the stability and guarantee a prescribed H∞performance level. The existing various iterative methods are known to converge lo-cally and do not necessarily achieve a global minimum for the disturbance attenuationlevel. This problem can be avoided by the proposed strategies.The robust H∞filtering problem for polytopic Delta operator systems is consid-ered. Based on the H∞performance criterion, two kinds of the filtering strategy is pre-sented. A structured polynomial parameter-dependent approach is proposed to solverobust H∞filtering problem, which is realized by carefully selecting the structure ofthe matrices involved in the products with system matrices. The matrix inequalitiesare obtained for the existence of admissible filters, and the designed filters can guar-antee the filtering error systems to be asymptotically stable and have a prescribed H∞disturbance attenuation performance for all admissible uncertain parameters. The fil-ter design approaches based on the polynomial parameter-dependent idea is much lessconservative than the conventional H∞filter design methods.