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The seemingly straightforward stability issue in three-dimensionalhomogeneous continuous piecewise linear systems with two linearzones is considered. The only equilibrium at the origin, being inthe separation plane of the linear zones, has two linearizationmatrices. For the important case where both matrices have complexeigenvalues with the whole spectrum in the left half plane, thepossible counter-intuitive instability of the origin is proved.Some sufficient conditions for the global asymptotic stability ofsuch systems are also shown.
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Carmona et al. (2006) studied this question.
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