External dynamical equivalence of analytic control systems

Abstract

Theory of systems on homogeneous time scales unifies theories of continuous-time and discrete-time systems. The characterizations of external dynamical equivalence known for continuous-time and discrete-time systems are extended here to systems on time scales. Under assumption of uniform observability, it is shown that two analytic control systems with output are externally dynamically equivalent if and only if their delta universes are isomorphic. The delta operator associated to the system on a time scale is a generalization of the differential operator associated to a continuous-time system and of the difference operator associated to a discrete-time system. © 2008 Springer-Verlag Berlin Heidelberg.