Abstract

Examples of discontinuous switched linear systems built by composing stable systems are known. In this talk, three-dimensional homogeneous continuous piecewise linear systems composedb by two linear systems sharing a boundary plane are considered. If the two linearization matrices are non-singular, then the only equilibrium point is at the origin, which is in the separation plane of the linear regions. For the important case where both matrices have complex eigenvalues and their whole spectra are in the open left half plane of the complex plane, the posible counterintuitive instability of the origin is analytically proved. Examples of unstable continuous switched linear systems with just two stable components are shown.