Model Reduction of Bilinear System Using Balanced Singular Perturbation
This paper is concerned with generalize model order reduction using the balanced singular perturbation for bilinear system. We first transform the bilinear system to be balanced realization and then we divide the state into the fast and the slow mode. By setting the velocity of the fast mode equal to zeros, we obtain the bilinear system with lower order. To verify the proposed method, the simulation is carried out on a nonlinear RC circuit and the results show that this method is able to approximate a high order model is similar to the balanced truncation method.
KeywordsBilinear system model order reduction balanced singular perturbation
Unable to display preview. Download preview PDF.
- 2.Al-Baiyat, S., Bettayeb, M.: A New Model Reduction Scheme for K-Power Bilinear Systems. In: Proceeding of the 32nd Conference on Decision and Control, pp. 22–27 (1993)Google Scholar
- 5.Balakrishnan, V., Su, Q., Koh, C.: Efficient Balance-and-Truncate Model Reduction for Large Scale Systems. ECE Technical Reports, Purdue University, Paper 31 (2000)Google Scholar
- 10.Gray, W.S., Verriest, E.I.: Algebraically Defined Gramians for Nonlinear Systems. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 3730–3735 (2006)Google Scholar
- 11.Hamberg, J., Resensi, O.: Modern Tools for Control of Nonlinear Systems. Swedish Defence Research Agency (September 2005)Google Scholar
- 12.Hartmann, C., et al.: Balanced Model Reduction of Bilinear Systems with Application to Positive Systems (2010) (reprint)Google Scholar
- 13.Lee, S.H., Lee, K.: Bilinear Systems Controller Design with Approximation Techniques. Journal of the Chungcheong Mathematical Society 18(1), 101–116Google Scholar
- 17.Mohler, R.R.: Nonlinear Systems: Volume II, Applications to Bilinear Control. Prentice Hall (1991)Google Scholar