Transfer matrices, realization, and control of continuous-time linear time-varying systems via polynomial fractional representations

AbstractAn algebraic theory of transfer matrices, fractional representations, and control for linear continuous-time time-varying systems based on the realization theory of input-output maps is given. It is shown for the first time that the realization of such systems specified by an abstract input-output map (as a module homomorphism over noncommutative polynomial rings) can be established using an abstract Kalman input-output map defined over a ring of skew polynomials with time-varying coefficients. It is shown that, in fact, transfer matrices can be defined as formal powe