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$$\ell_1$$-induced norm and controller synthesis for positive 2D systems with multiple delays. (English) Zbl 1447.93154
Summary: This paper addresses the problem of $$\ell_1$$-induced controller design for positive two-dimensional (2D) systems with multiple delays. An analytical method is presented to calculate the exact value of $$\ell_1$$-induced norm for positive 2D delayed systems. Necessary and sufficient conditions for asymptotical stability and $$\ell_1$$-induced performance are first derived for the addressed system. Then, based on the singular value decomposition (SVD) technique, controllers are designed to guarantee the asymptotic stability with a prescribed $$\ell_1$$-gain performance level. Those characterizations are formulated in the form of linear programming (LP). Finally, two examples are provided to show the effectiveness and correctness of the theoretical results.
##### MSC:
 93C28 Positive control/observation systems 93D20 Asymptotic stability in control theory 93C43 Delay control/observation systems 90C05 Linear programming
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