Application of the operational matrix of differentiation for the identification of time-varying linear systems using polynomial series

The operational matrix of differentiation is used for the parameter identificaton of a class of time-varying linear systems using polynomial series. The main advantage of this approach is that it does not require the introduction of the initial conditions of the system, as it becomes necessary with the use of the operational matrix of integration. In this way the resulting algorithm is considerably simpler. The operational matrix of a polynomial series transformation is also used and may transform a given orthogonal polynomial series into another. This matrix simplifies considerably the computation of the product and coefficient matrices required for the identification of time-varying systems. Several characteristic examples are considered for the illustration of the effectiveness of the method.