Algebraic and topological aspects of quantitative feedback theory

摘要

The design methodology of quantitative feedback theory (QFT) is by now a highly developed technique and has been applied with success to several industrial and military systems involving highly uncertain plants and disturbanes. However, the absence of theoretical rigor in some QFT statements have been challenged and assumed to imply that the basic theory is at best incomplete. Recently, it, was shown that the basic assumptions of QFT are not only correct and logically consistent, but also subsume and predate some of the more recent necessary conditions for reliable robust stabilization based on H/sup /spl infin//- optimization by about 20 years. The paper continues this algebraic and topological redevelopment of QFT. In particular, the basic description of uncertainty in QFT will be shown to imply the topological path connectedness of the underlying uncertain plant transfer matrix family; and hence a necessary condition for robust stabilizability. Furthermore, the admissibility of diagonal feedback compensators for some QFT problems implies the absence of unstable decentralized fixed modes with respect to diagonal constant output feedback for the entire uncertain plant transfer matrix family. These results indicate some ways for improving the efficiency and user-friendliness of current QFT-CAD software.