This paper is concerned with the analysis of a singularity that can occur in three-dimensional discontinuous feedback control systems. The singularity is the two-fold — a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show that such a singularity cannot occur in classical single-input single-output systems in the Lur’e form. It is, however, a potentially dangerous phenomenon in multiple-input multiple-output switched control systems. The theoretical derivation is illustrated by means of a representative example.
Colombo, A., di Bernardo, M., Fossas, E., & Jeffrey, M. R. (2010). Teixeira singularities in 3D switched feedback control systems. Systems & Control Letters, 59(10), 615-622. https://doi.org/10.1016/j.sysconle.2010.07.006