Duality in time-varying linear systems: A module theoretic approach

Using elementary module theory, an intrinsic definition of the dual (or adjoint) of a generalized time-varying linear system is given. With this, the duality of controllability and observability is recovered from their intrinsic module theoretical definitions. The duality of state feedback and output injection is discussed both in the static case and for its quasistatic generalization. Related Brunovsky type canonical forms are derived in the quasistatic case. The corresponding controllability indices and their duals the observability indices are defined intrinsically.