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September  2006, 16(3): 689-703. doi: 10.3934/dcds.2006.16.689

The continuous matching of two stable linear systems can be unstable

V. Carmona 1, , E. Freire 1, , E. Ponce 1, and  F. Torres 1,

1. 

Departamento Matemática Aplicada II, Escuela Técnica Superior de Ingenieros. Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain, Spain, Spain, Spain

Received  February 2005 Revised  August 2006 Published  August 2006

The seemingly straightforward stability issue in three-dimensional homogeneous continuous piecewise linear systems with two linear zones is considered. The only equilibrium at the origin, being in the separation plane of the linear zones, has two linearization matrices. For the important case where both matrices have complex eigenvalues with the whole spectrum in the left half plane, the possible counter-intuitive instability of the origin is proved. Some sufficient conditions for the global asymptotic stability of such systems are also shown.
Keywords: Piecewise linear systems, invariant manifolds, stability..
Mathematics Subject Classification: Primary: 37C70; Secondary: 34A34, 37C7.
Citation: V. Carmona, E. Freire, E. Ponce, F. Torres. The continuous matching of two stable linear systems can be unstable. Discrete and Continuous Dynamical Systems, 2006, 16 (3) : 689-703. doi: 10.3934/dcds.2006.16.689
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