Title: An exterior-point approach to the output feedback mixed H₂/H_∞ controller design

Authors: Yasushi Kami; Eitaku Nobuyama; Yuki Imanishi

Addresses: Department of Electrical and Computer Engineering, National Institute of Technology, Akashi College, Hyogo, Japan ' Department of Systems Design and Informatics, Kyushu Institute of Technology, Fukuoka, Japan ' Department of Applied Mathematics and Physics, Graduate School of Informatics Kyoto University, Kyoto, Japan

Abstract: This paper treats the mixed H₂/H_∞ control problem and the mixed H₂/H_∞ controller is very useful in the sense that it achieves a robust stability against uncertainties and a specified transient performance simultaneously. However it is difficult to find such controllers, because this control problem can be described as a non-convex problem. In order to get feasible solutions some interior-point approaches have been proposed. However, this approach cannot be carried out in the case that, initial feasible solutions are not found. In this paper an exterior-point approach to the mixed H₂/H_∞ control problem is proposed. One of properties of our approach is to be able to use any stabilising controllers as an initial point, even if they are not feasible solution of the problems. Hence our approach can overcome the drawback of the interior-point approaches. The efficiency of our approach is shown by numerical examples.

Keywords: mixed H₂/H_∞ control; exterior-point approach; output feedback; iterative method; controller sequence; partial derivative; H₂ norm; H_∞ norm; non-common Lyapunov variables; LMI.

DOI: 10.1504/IJAMECHS.2017.095889

International Journal of Advanced Mechatronic Systems, 2017 Vol.7 No.5, pp.311 - 318

Received: 10 Jul 2017
Accepted: 18 Jun 2018
Published online: 25 Oct 2018 *

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