The simulation problem for high order linear differential systems. (Q1412495)

This paper addresses linear differential equations of the form \(R (\frac{d}{dt}) w = M (\frac{d}{dt}) f\), with constant coefficients, where \(R\), \(M\) are polynomial matrices, and \(w\), \(f\) are distributions. The authors investigate their solvability in a behavioral sense, as well as the index relating smoothness of \(f\) and \(w\), and also the compatibility of initial conditions of the form \(S(\frac{d}{dt}) w(0) = Ta\), \(S\) being a polynomial matrix, \(T\) a real matrix, and \(a\) a real vector. The results extend some properties of linear, time-invariant differential-algebraic equations (DAEs).