Identification of multi-delay systems using orthogonal hybrid functions in state space environment

Abstract

In this paper, a set of orthogonal hybrid functions (HF) is utilised for the identification of non-homogeneous as well as homogeneous multi-delay systems. The HF set works with function samples and reconstructs a function in a piecewise linear manner. This reduces the mean integral square error (MISE) of approximation and also the computational burden compared to other competitive methods like Walsh analysis, block pulse analysis, etc. in general. The presented technique uses a simple algorithm for time-delay system identification. After introducing the HF domain approximation and integration, the HF domain theory of identification of multi-delay systems is presented. To support the theory, many numerical examples are treated to identify both first and second order delay systems. The presented tables and graphs prove that the results obtained are highly reliable to establish the validity of the proposal.