A convolution identification approach for systems with delayed and arbitrary entries via polynomial functions

In this paper, an online delay identification method of continuous-time linear systems with unstructured inputs is proposed. This approach is based on a distributional algebraic technique and a convolution approach. Such technique leads to simple realization schemes involving derivation, multipliers by polynomial functions and integrators. In the case of arbitrary inputs, the formulation of the identification problem requires the addition of a cross convolution step. The proposed method enables a fast delay estimation under initial conditions and static disturbance. Moreover, an application to a suspension system model is provided. In this instance, the input and the output trajectories are arbitrary and have a close and abundant crossing zero. Simulation studies show the performances of the proposed approach.