\(\ell_1\)-induced norm and controller synthesis for positive 2D systems with multiple delays.

*(English)*Zbl 1447.93154Summary: 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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\textit{J. Fu} et al., J. Franklin Inst. 357, No. 12, 7904--7920 (2020; Zbl 1447.93154)

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