多次元システム強安定化の数理(自然科学)

概要

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We consider the stabilization problems of n-D linear systems described by multivariate rational transfer matrices. A plant is said stable if all the entries of the transfer matrix are analytic on the unit polydisc in the n-D complex space. A plant is said to be strongly stabilizable if there exists a stable compensator that stabilizes it via some standard feedback configuration. For an 1-D plant, it can be shown that a complex stable stabilizing compensator always exists. But this is not true for an n-D (n>1) plant. Shankar derived a topological condition for the existence of a complex stable stabilizer for an n-D SISO (single input single output) plant. Ying introduced a concept of "sign" of a real function on complex variety, and showed that some constant sign condition is necessary for a real n-D SISO plant to be stabilizable by a real stable compensator. This condition turns out to be a generalization of Youla's parity interlacing property for 1-D system. In this paper we present new results concerning strong stabilizability of MIMO n-D systems. The main contribution are some mathematical theorems that extend Ying's result. Applying these theorems, we are able to give necessary and sufficient conditions for the existences of complex or real stable stabilizing compensators for n-D MISO (multi-input single output) and SIMO (single input multi-output) plants.
岐阜大学の論文
1998-03-26