本計畫針對離散時間、線性、非時變正值系統，研究動態與靜態輸出回授設計，以達到閉迴路系統為正值、穩定且具備某水準的 性能，並且著重在控制器可具任意指定結構。在不同的寬鬆假設之下，本計畫得到線性矩陣不等式（linear matrix inequality, LMI）形式的有解條件，其可用於求解任意階數與任意指定輸出/輸入結構的控制器(包括靜態輸出回授與無結構限制的控制器)。以萊斯利（Leslie）系統為例的模擬結果證實了本計畫所提方法的確有效。
In this project, we aim at investigating the H-infinity dynamic output controller synthesis with respect to positive systems. Despite the maturity of the H-infinity control theory of general linear systems, it is until very recent that the bounded real lemma for positive systems has been developed. As far as we know the results concerning this controller design issue is rare. The existing ones all adopt static state feedback control law, and no result concerning dynamic output feedback has been found in the open literature. Therefore, we’d like to investigate the following two issues: Problem A. H-infinity dynamic output feedback control of linear systems with closed-loop positive constraint; Problem B. Weighted H-infinity dynamic output feedback control of linear systems with closed-loop positive constraint. With our new developing skillful techniques, we will make the most use of the special properties of positive systems to derive the solvability conditions for the problems. The decentralized control design for Problem A will be employed to problem B, Together with the generalized Kalman-Yakubovich-Popov lemma we will provide a new weighted H-infinity control method that is quite different from the tradition one (a two-phase design). The weighting functions are not chosen a priori but are synthesized simultaneously with the controllers. While this new technical treatment may offer a chance for finding better solutions to both of the problems, it also facilitates the search of performance weights for the weighted H-infinity control problem. Numerical experiment will be conducted to verify the effectiveness of the design methods. Finally, we will devote ourselves to the establishment of the hardware verification platform in order to verify the efficacy of the proposed controllers.
