H_∞Reduced-Order Filtering For Positive Systems

In recent years, there has been an increasing interest in the study of positive system since thepositive system models are often encountered in various fields of sociology, economics, industrial.And many important results have been obtained. However, there is less research on H∞reduced-order filtering for positive systems. So based on the research status on positive systems and H∞reduced-order filtering, this paper studied the problem of designing H∞reduced-order filteringfor positive singular systems and positive time-delay systems. The main works of this thesis areas follows:(1) The problems of designing H∞reduced-order filtering for positive continuous and dis-crete singular systems are investigated, respectively. Firstly, the filtering error system is repre-sented as a new singular system by means of the system augmentation approach. Then, basedon the new singular system, a novel necessary and sufcient condition ensuring the filtering errorsystem to be asymptotically stable and have a prescribed H∞performance is established. Basedon this necessary and sufcient condition, an existence condition of filtering is given in termsof linear matrix inequalities. Finally, an corresponding iterative algorithm of solving filteringis presented. And a number example is shown to illustrate the efectiveness of the proposedmethod.(2) The problems of designing H∞reduced-order filtering for positive continuous and dis-crete time-delay systems are investigated, respectively. Our attention is focused on designingthe positive H∞reduced-order filtering without time-delay for the positive time-delay systemsin such a way that the filtering error system with time-delay is stable with a prescribed H∞per-formance. Firstly, the filtering error system with time-delay is represented as a singular systemwith time-delay by means of the system augmentation approach. Then, based on the singularsystem with time-delay, a novel sufcient condition ensuring the filtering error system with time-delay to be asymptotically stable and have a prescribed H∞performance is established. Basedon this sufcient condition, an existence condition of filtering is given in terms of linear matrix inequalities. Finally, an corresponding iterative algorithm of solving filtering is presented. Anda number example is shown to illustrate the efectiveness of the proposed method.