Parameter estimation for a class of time‐varying systems with the invariant matrix

Abstract This article is concerned with the identification of time‐varying systems. Differently from the conventional polynomial approximation approaches, the changing laws of the time‐varying parameters are considered to build the identification model for the time‐varying systems. Specifically, the concept of the invariant matrix is put forward to characterize the time‐varying parameters and to establish the state‐space model with regard to the system parameters. Then this article proposes a stacked state estimation algorithm to achieve the time‐varying parameter estimation. Moreover, for the purpose of enhancing the computational efficiency, a detached state estimation algorithm is proposed by reducing the dimension of the state vector to reconstruct the state equation. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed algorithms.