TY - GEN

T1 - Some conditions for convexifying static H∞ control problems

AU - Ebihara, Yoshio

AU - Peaucelle, Dimitri

AU - Arzelier, Denis

N1 - Funding Information:
⋆ This work is supported in part by the Ministry of Education, Culture, Sports, Science and Technology of Japan under Grant-in-Aid for Young Scientists (B), 21760328.

PY - 2011

Y1 - 2011

N2 - In this paper, we show that a set of static controllers satisfying a certain level of H∞ performance becomes convex when the underlying generalized plant satisfy several structural conditions. More precisely, we characterize such static H∞ controllers by an LMI with the controller parameters being kept directly as decision variables. The conditions on the generalized plant are not too strict as illustrated by the fact that a sort of mixed sensitivity problems indeed satisfies these conditions. In addition, for the generalized plant of interest, we prove that full-order dynamical H∞ controllers can be characterized by an LMI with simple change of variables. In stark contrast to known LMI formulations, the change of variables does not involve coefficient matrices of the generalized plant. This property is promising when dealing with a whole variety of robust control problems. As an illustration, the real μ synthesis problem is discussed.

AB - In this paper, we show that a set of static controllers satisfying a certain level of H∞ performance becomes convex when the underlying generalized plant satisfy several structural conditions. More precisely, we characterize such static H∞ controllers by an LMI with the controller parameters being kept directly as decision variables. The conditions on the generalized plant are not too strict as illustrated by the fact that a sort of mixed sensitivity problems indeed satisfies these conditions. In addition, for the generalized plant of interest, we prove that full-order dynamical H∞ controllers can be characterized by an LMI with simple change of variables. In stark contrast to known LMI formulations, the change of variables does not involve coefficient matrices of the generalized plant. This property is promising when dealing with a whole variety of robust control problems. As an illustration, the real μ synthesis problem is discussed.

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U2 - 10.3182/20110828-6-IT-1002.00748

DO - 10.3182/20110828-6-IT-1002.00748

M3 - Conference contribution

AN - SCOPUS:84866760312

SN - 9783902661937

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 9248

EP - 9253

BT - Proceedings of the 18th IFAC World Congress

PB - IFAC Secretariat

ER -