Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

Khalid Badie, Mohammed Alfidi, Fernando Tadeo and Zakaria Chalh

International Journal of Systems Science, 2020, vol. 51, issue 3, 440-460

Abstract: The design of delay-dependent robust $H_{\infty } $H∞ controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to $H_{\infty } $H∞ performance analysis and robust $H_{\infty } $H∞ controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Date: 2020
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DOI: 10.1080/00207721.2020.1716102

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