拡張された線形化法に基づく一般的ロバスト制御系設計(<特集>通信と制御)

概要

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This paper proves that a certain class of nonconvex matrix inequalities is equivalent to linear matrix inequalities (LMIs) plus a nonconvex rank constraint. From the equivalence, this paper proposes two heuristic algorithms, that is extended linearization algorithms, to solve LMIs with a rank constraint using LMI-based approach. Reliability and efficiency of the algorithms are investigated statistically, and then extensive numerical experiments will indicate that the algorithms have a decent performance from the viewpoint of computation in comparison with the existing method: the alternating projection method. It is also important that our approaches can be applied to a large number of other rank-minimization problems over LMIs, for example, the robust well-posedness problem which is an extension of general robust control problems.
2005-06-15