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On the internal stability and asymptotic behavior of 2-D positive systems. (English) Zbl 0891.93046
The internal stability of homogeneous 2-D linear systems described by a nonnegative pair $$(A, B)$$ is characterized in terms of the spectrum of the matrix sum $$A+B$$. Special classes of separable matrix pairs and those endowed with property $$L$$ or with one-dimensional characteristic polynomial are analyzed. The problem of asymptotic free evolution of 2-D positive linear systems is also considered.

##### MSC:
 93C35 Multivariable systems, multidimensional control systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C05 Linear systems in control theory
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