TY - GEN
T1 - Strong feasibility of the dual problem of linear matrix inequality for H∞ output feedback control problem
AU - Waki, Hayato
AU - Sebe, Noboru
N1 - Funding Information:
The first author was supported by JSPS KAK-ENHI Grant Numbers JP22740056, JP26400203, and JP17H01700.
Publisher Copyright:
© 2018 The Society of Instrument and Control Engineers - SICE.
PY - 2018/4/2
Y1 - 2018/4/2
N2 - Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H∞ output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.
AB - Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H∞ output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.
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U2 - 10.23919/SICEISCS.2018.8330155
DO - 10.23919/SICEISCS.2018.8330155
M3 - Conference contribution
AN - SCOPUS:85049335246
T3 - SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
SP - 47
EP - 53
BT - SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 SICE International Symposium on Control Systems, SICE ISCS 2018
Y2 - 9 March 2018 through 11 March 2018
ER -