External dynamical equivalence of time-varying nonlinear control systems on time scales

摘要

Theory of systems on homogeneous time scales unifies theories of continuous-time and discrete-time systems. The characterisations of external dynamical equivalence known for continuous-time and discrete-time systems with outputs are extended to time-varying systems on time scales. The main result says that two uniformly observable nonlinear control systems are externally dynamically equivalent if and only if their delta universes are properly isomorphic. The delta operator associated to the given system on a time scale is a generalisation of the differential operator associated to a continuous-time system and of the difference operator associated to a discrete-time system.