TY - JOUR
T1 - Positive Definiteness in Linear Matrix Inequality Problem for H-Infinity Output Feedback Control Problem
AU - Waki, Hayato
N1 - Funding Information:
Manuscript received October 24, 2018; revised January 7, 2019; accepted February 3, 2019. Date of publication February 8, 2019; date of current version February 23, 2019. The work of H. Waki was supported in part by Japan Society for the Promotion of Science KAKENHI under Grant JP26400203 and Grant JP17H01700, and in part by the Toyota RIKEN Specially Promoted Research Program [PI: Yoshio Ebihara (Kyoto University)]. Recommended by Senior Editor J. Daafouz.
Publisher Copyright:
© 2017 IEEE.
PY - 2019/4
Y1 - 2019/4
N2 - We focus on the positive definiteness in the linear matrix inequality (LMI) problem obtained from H ∞ output feedback control problem. In particular, we provide a necessary condition for an inequality constraint of the LMI problem, which is called the coupling constraint, to strictly hold at optimal solutions. It is reasonable to expect that the condition does not hold for most generalized plants. In other words, the strict inequality at the optimal solutions rarely happens in H ∞ output feedback control for most generalized plants. Thus, we must apply remedies for constructing a controller after solving the LMI problem.
AB - We focus on the positive definiteness in the linear matrix inequality (LMI) problem obtained from H ∞ output feedback control problem. In particular, we provide a necessary condition for an inequality constraint of the LMI problem, which is called the coupling constraint, to strictly hold at optimal solutions. It is reasonable to expect that the condition does not hold for most generalized plants. In other words, the strict inequality at the optimal solutions rarely happens in H ∞ output feedback control for most generalized plants. Thus, we must apply remedies for constructing a controller after solving the LMI problem.
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U2 - 10.1109/LCSYS.2019.2898385
DO - 10.1109/LCSYS.2019.2898385
M3 - Article
AN - SCOPUS:85061550039
SN - 2475-1456
VL - 3
SP - 446
EP - 451
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 2
M1 - 8637724
ER -