UBC Theses and Dissertations
Stabilization via smooth partitions, transversality and graphs Glaum, Michael
With the aim of circumventing the difficulty in constructing Liapunov functions, a strategy for the design of static stabilizing feedback control laws of nonlinear systems is proposed. The basic method is to partition the state space and to find all controls so that the closed-loop dynamics are transverse or coincident to the partition edges. Stability is analyzed through the directed graph whose vertices are the subsets of the partition and whose arcs are consistent with the transversality. A strategy for the choice of partition is proposed using computable Pfaffian systems.
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