The use of modulating functions for identification of continuous systems with time-varying parameters

In the paper the use of modulating functions for the optimal identification of the structure and parameters of continuous linear systems is presented. The modulating functions with compact support [0, h] are used in convolution filter for transformation of input/output signal derivatives. Based on pre-filtered functions continuous moving window [t-T, t] is used for on-line identification of piecewise constant parameters Θ changes of linear system. Optimal quadratic method for identification is presented – with the use of quadratic constraints on parameters Θ. The numerical results of some examples are shown.