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.

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

VL - 3

SP - 446

EP - 451

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 2

M1 - 8637724

ER -