IEEE Transactions on Automatic Control, Vol.55, No.10, 2282-2297, 2010
Realization Theory for Linear Hybrid Systems
The paper develops realization theory for linear hybrid systems, i.e., hybrid systems in continuous-time without guards whose continuous dynamics is determined by linear control systems and whose discrete dynamics is determined by a finite-state automaton. We will formulate necessary and sufficient conditions for the existence of a realization. We will show that minimality is equivalent to observability and span-reachability, and that minimal systems are isomorphic. In turn, observability and span-reachability can be characterized by rank conditions.
Keywords:Linear hybrid systems (LHS)