An algebraic analysis approach to linear time-varying systems

^** Email: zerz{at}mathematik.uni-kl.de This paper introduces an algebraic analysis approach to lineartime-varying systems. The analysis is carried out in an ‘almosteverywhere’ setting, i.e. the considered signals are smoothexcept for a set of measure zero, and the coefficients of thelinear ordinary differential equations are supposed to be rationalor meromorphic functions. The methodology is based on a normalform for matrices over the resulting ring of differential operators,which is a non-commutative analogue of the Smith form. Thisis used to establish a duality between linear time-varying systemson the one hand and modules over the ring of differential operatorson the other. This correspondence is based on the fact thatthe signal space is an injective cogenerator when consideredas a module over this ring of differential operators.