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Dynamic Feedback Equivalence of Time-Variant Control Systems on Homogeneous Time Scales

Zbigniew Bartosiewicz, Ewa Pawluszewicz


The problem of weak dynamic feedback equivalence of nonlinear time-variant control systems on homogeneous time scales is studied. Besides the state and control transformations, also time transformation is allowed, so equivalent systems may be defined on different time scales. The delta algebra of the system is introduced. The main result says that two systems defined on time scales are weakly dynamically feedback equivalent if and only if their delta algebras are properly isomorphic. This is an extension of the earlier result on dynamic feedback equivalence of time-invariant systems.

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