H_∞Model Reduction For 2-d Positive System And Designing Of The Output Feedback Controller

In recent years, because of the wide applications of positive system in many areas, such asbiomedical, industrial engineering, behavioral science, economics and so on. the positive systemhas received the attention of many scholars at home and abroad, and many encouraging resultshave been achieved. However, there are little results about the H_∞model reduction and thecontroller design problem for positive systems. Therefore, based on the general situation of thestudy of the positive system and the 2-D system, we focus on the problem of H_∞model reductionfor 2-D positive system and the problem of designing the static output feedback controller forthe positive linear continuous-time systems. The contents are as follows:1) The H_∞model reduction for positive 2-D system based on the Roesser model is con-sidered. Firstly, the error system is equivalent to the singular system by means of the systemaugmentation approach. Secondly, on the basis of singular system, a new sufcient conditionis obtained to ensure the error system to be asymptotically stable and satisfy the H_∞perfor-mance. Then, based on the sufcient condition, a sufcient condition for that model reductionis proposed in form of linear matrix inequalities. Finally, the iterative algorithm is given tocompute the reduced-order system matrices, and the efectiveness of the proposed method canbe shown by a numerical example.2) The H_∞model reduction for positive 2-D system with time-delay based on the Roessermodel is considered. Firstly, the error system with time-delay is equivalent to the singularsystem with time-delay by means of the system augmentation approach. Secondly, on the basisof singular system with time-delay, a new sufcient condition is obtained to ensure the errorsystem with time-delay to be asymptotically stable and satisfy the H_∞performance. Then,based on the sufcient condition, a sufcient condition for that model reduction is proposed inform of linear matrix inequalities (LMI). Finally, the iterative algorithm is given to compute the reduced-order system matrices, and the efectiveness of the proposed method can be shown bya numerical example.3) The problem of designing the static output feedback controller for the positive linearcontinuous-time systems is considered. the static output feedback controller is designed to makethe closed-loop system asymptotically stable. Firstly, the closed-loop system is equivalent tothe singular system by means of the system augmentation approach. Secondly, on the basis ofsingular system, a new necessary and sufcient condition is obtained to ensure the closed-loopsystem to be asymptotically stable . Then, based on this necessary and sufcient condition, adesign approach for the static output feedback controller for the positive linear continuous-timesystems is proposed in form of linear matrix inequalities (LMI). Finally, the efectiveness of theproposed method can be shown by a numerical example.