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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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