Adaptive rational orthogonal basis functions for identification of continuous-time systems

In this article, we present two algorithms for identification of continuous-time linear time-invariant systems in frequency domain. These algorithms are constructed in terms of continuous rational orthogonal basis functions. First, a two-stage algorithm is developed through one-by-one selection of poles for the basis functions, and such consecutive selection is easy to realize. Next, a direct algorithm is proposed to select poles for the rational orthogonal basis functions. Different poles result in different bases and these selections guarantee that better approximations can be reached. For different systems, there are different sequences of poles selected for basis functions, which shows the adaptivity of the proposed algorithms. A numerical example is given to show that the proposed algorithms are useful. Also, in this example, comparison is made with the method that uses rational orthogonal basis functions in which all poles of the basis functions are true poles of the original system.