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**LMI approach to stability of 2D positive systems.**
*(English)*
Zbl 1169.93022

Summary: The asymptotic stability of positive 2D linear systems with delays (systems of order higher one) described by the Roesser model, the 2D Fornasini-Marchesini models and the general model is addressed. It is shown that the Linear Matrix Inequalities (LMIs) can be used to checking the asymptotic stability of the positive 2D systems. Using LMI approach necessary and sufficient conditions for the asymptotic stability of the positive 2D systems with delays are established. The efficiency of the LMI approach is demonstrated on numerical examples of positive 2D linear systems with delays.

### MSC:

93D20 | Asymptotic stability in control theory |

15B48 | Positive matrices and their generalizations; cones of matrices |

15A39 | Linear inequalities of matrices |

93C05 | Linear systems in control theory |

93C65 | Discrete event control/observation systems |

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\textit{T. Kaczorek}, Multidimensional Syst. Signal Process. 20, No. 1, 39--54 (2009; Zbl 1169.93022)

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### References:

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