Hierarchical hybrid control systems: a lattice theoretic formulation

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 S. Following the formulation of the notions of between-block and in-block controllable hybrid partition machines, the lattice HIBC(S) of hybrid in-block controllable partition machines is defined and investigated. Based on these constructions, the definition and properties of hierarchical-hybrid control systems are presented together with an example.