Algebraic theory for time variant linear systems: modes, minimality and reachability and observability of interconnected systems

Realization theory for time-invariant systems is extended, via the algebraic framework of skew polynomial rings. We emphasize the notions of greatest common divisors, the least common (left and right) multiples, the Bezout identity, and the use of these in resolving the modes for a time-varying system. Different canonical representations of the noncommutative polynomials lead directly to the canonical realizations for time varying systems. The PBH test is extended to time-varying systems, and its application for testing reachability and observability of interconnected systems is given