Y-J. Wei, P.E. Caines The notion of dynamical consistency is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system [IMAGE ]. The basic notions of between-block and in-block controllable hybrid partition machines are given in this work and the lattice [IMAGE ] of hybrid in-block controllable partition machines have been defined. Based on these constructions, the properties of hierarchical-hybrid feedback control systems have been investigated and applied to a set of examples.