Necessary and sufficient conditions for global asymptotic stability of a class of bimodal systems with discontinuous vector fields

Abstract

In this article, we derive the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in R-3, where first mode has complex eigenvalues and the second mode has only real eigenvalues. The vector field is allowed to be discontinuous on the switching plane. The effect of discontinuity is illustrated by two examples.