Continuous-time system representation with exact macro-difference expressions

A macro-difference equation representation is proposed which is a mixture of finite-difference quotients and integrals over finite time intervals. The choice of the micro or sampling interval length (for the numerical integration accuracy and representation bandwidth) and the choice of the macro interval length (for numerical conditioning/accuracy of the difference quotients and of the resulting equations) are independent. This approach does not need the assumption (which in practical situations is quite unnatural) of zero initial conditions.