Stability of Planar Piecewise Linear Systems: A Geometric Condition
Résumé
Any planar piecewise linear (two-state, multi-modal) system is shown to be globally asymptotically stable just in case each linear mode satisfies certain conditions that solely depend on how its eigenvectors stand relative to the cone on which it is defined. The conditions are in terms of the eigenvalues, eigenvectors, and the cone.
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