Zero dynamics, zeros and reachable/observable structure in MIMO LTI systems

We provide an analysis of system dynamics in sliding along the switching manifold. A general form of system trajectories on the switching surface as well as a general form of continuous controls which hold the system trajectories on the switching surface are obtained. As it is shown, the behaviour of the system in sliding is governed by a matrix which fully characterizes system zeros. When the system is uncontrollable or unobservable, the switching surface can be decomposed into the union of pairwise disjoint subsets and this decomposition is induced by system reachable/observable structure.