An efficient hybrid reduction method for time-delay systems using Hermite expansions

ABSTRACT

This paper presents an efficient model reduction method for time-delay systems in the time domain. We expand the systems under a Hermite polynomial basis and show that Hermite coefficients of the expansion are determined by a linear equation, thus can be calculated efficiently. Such linear relationship is well taken in the projection methods of model reduction, and reduced models are generated to preserve a desired number of Hermite coefficients in the time domain, in contrast to other existing techniques which aim at approximating the transfer function of time-delay systems in the frequency domain. We also exploit two-sided projections for time-delay systems, leading to a hybrid reduction method which generates reduced models sharing the nice properties both in the time and frequency domains. Two numerical examples illustrate the feasibility and effectiveness of the approach.

KEYWORDS:

• Time-delay systems
• model reduction
• Hermite polynomials
• function expansion

Acknowledgments

The authors are very much indebted to the referees for their valuable comments and suggestions which improve this paper significantly. The authors sincerely thank Dr Maryam Saadvandi for the discussion on details of the dominant poles algorithm.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (NSFC) [grant number 11401472], [grant number 11371287]; and the Natural Science Foundation of Shaanxi Provincial [grant number 2017JM1019].