Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 96, Issue 11, Pages 2937-2943Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2022.2118176
Keywords
Negative imaginary system; output feedback control; H-2 control; semidefinite programming
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This paper studies the problem of designing a static output feedback H-2 negative imaginary controller. A linearisation-based method is proposed to overcome the difficulty of solving constraints, and an iterative algorithm is provided to compute the desired controller. The results are illustrated through numerical examples.
In this paper, the problem of designing static output feedback (SOF) H-2 negative imaginary controller has been studied. Because the constraints brought by negative imaginary (NI) property and H-2 performance are a set of bilinear matrix inequalities (BMIs), designing an SOF NI controller with H-2 performance is a non-trivial problem. To overcome the difficulty of solving BMIs, a linearisation-based method is proposed. First, a necessary and sufficient condition is established, where the constraints of NI property and H-2 performance are reformulated as similar forms. Second, inspired by the semi-definite programming, the derived condition is converted to the difference between two convex functions. Then a linearised iterative algorithm with initialisation process is provided to compute the desired SOF H-2 NI controller. Finally, two numerical examples are presented to illustrate the proposed results.
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