A brief review and insights into matrix inequalities for H∞ static-output-feedback control and a local optimal solution

Zhi-Yong Feng, Jinhua She and Li Xu

International Journal of Systems Science, 2019, vol. 50, issue 12, 2292-2305

Abstract: This paper first gives a brief review of four kinds of matrix inequalities and two open problems about $H_\infty $H∞ static-output-feedback (SOF) control of continuous-time systems. Then, by clarifying the relationships among those matrix inequalities, the two open problems are proved to be essentially equivalent to a problem of choosing a coordinate transformation matrix (CTM). A new two-step optimisation method is established to solve this open problem. In the first step, a cone complementarity linearisation (CCL) method is utilised to solve the SOF-stabilisation problem so as to obtain a proper initial CTM. In the second step, a T-K iteration strategy is developed to optimise the choice of the CTM to locally solve the optimal continuous-time $H_\infty $H∞ SOF control problem. Numerical examples are given to demonstrate the effectiveness and benefits of the proposed method.

Date: 2019
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DOI: 10.1080/00207721.2019.1654008

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