This thesis introduces novel and significant results regarding the analysis and synthesis of positive systems, especially under l1 and L1 performance. It describes stability analysis, controller synthesis, and bounding positivity-preserving observer and filtering design for a variety of both discrete and continuous positive systems.

It subsequently derives computationally efficient solutions based on linear programming in terms of matrix inequalities, as well as a number of analytical solutions obtained for special cases. The thesis applies a range of novel approaches and fundamental techniques to the further study of positive systems, thus contributing significantly to the theory of positive systems, a "hot topic" in the field of control.

Inhalt
Introduction.- 1-induced Controller Design for Positive Systems.- L1-induced Output-Feedback Controller Synthesis for Interval Positive Systems.- Positive State-Bounding Observer for Interval Positive Systems.- Positive Filtering for Positive Systems under L1 Performance.- Controller and Filter Syntheses for Positive Takagi-Sugeno Fuzzy Systems under 1 Performance.- Conclusions and Future Work.