Laguerre functions approximation for model reduction of second order time-delay systems

This paper presents a Laguerre-based model reduction method for time-delay systems, which naturally retains the second-order-structure of original systems. We expand time-delay systems under the Laguerre function basis and show that Laguerre coefficients satisfy a special linear system and therefore can be calculated iteratively. Then reduced models are produced using projection methods, where projection matrices are defined in terms of the derived Laguerre coefficients, while properties on the preservation of Laguerre coefficients are proved elegantly based on the linear system corresponding to Laguerre coefficients. We also discuss the practical implementation of the approach. A high order Arnoldi procedure with memory saving is provided which leads to an efficient execution of our approach in practice. Numerical examples are simulated to illustrate the feasibility and efficiency of our approach.