Model reduction of linear time delay systems via a class of balanced truncation

This paper investigates the model order reduction problems for linear time-delay systems with known operating frequency interval. Firstly, a class of linear system model which match the linear time-delay model exactly at the middle frequency. Then, a new middle frequency dependent balanced truncation algorithm was developed. The obtained reduced model approximate the original high-order model very well at the middle frequency and the frequency interval nearby, and the error bound at the middle frequency also established. Furthermore, the stability-preserving design conditions also derived . Finally, a numerical example was carried out to illustrate the effectiveness and advantages.