Sliding modes of high codimension in piecewise-smooth dynamical systems

Abstract We consider piecewise-smooth dynamical systems, i.e., systems of ordinary differential equations switching between different sets on distinct domains, separated by hyper-surfaces. As is well-known, when the solution approaches a discontinuity manifold, classical may cease to exist. For this reason, starting with pioneering work Filippov, concept weak (also known as sliding mode) has been introduced and studied. Nowadays, in close manifolds well understood, if manifold consists locally single hyper-surface or intersection two The present presents partial results codimension 3 higher.