Optimal time-weighted H 2 model reduction for discrete Markovian jump systems

作者: Minhui Sun , James Lam , Ningfan Zhong

DOI: 10.1109/CHICC.2014.6896510

关键词:

摘要: This paper considers the optimal time-weighted H 2 model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that norm corresponding error system minimized given MJLS. A new notation named defined first time. Then computational formula given. Based on this formula, gradient flow method proposed solve problem. Finally, numerical example used illustrate effectiveness approach.

参考文章(21)
Aivar Sootla, Semidefinite Hankel-Type Model Reduction Based on Frequency Response Matching IEEE Transactions on Automatic Control. ,vol. 58, pp. 1057- 1062 ,(2013) , 10.1109/TAC.2012.2218150
Wei Yang, Lixian Zhang, Ping Shi, Yanzheng Zhu, Model reduction for a class of nonstationary Markov jump linear systems Journal of The Franklin Institute-engineering and Applied Mathematics. ,vol. 349, pp. 2445- 2460 ,(2012) , 10.1016/J.JFRANKLIN.2012.05.010
Kwan Ho Lee, Biao Huang, H∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation International Journal of Systems Science. ,vol. 40, pp. 685- 693 ,(2009) , 10.1080/00207720902953102
Xiaojie Su, Ligang Wu, Peng Shi, Yong-Duan Song, ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems systems man and cybernetics. ,vol. 42, pp. 1574- 1585 ,(2012) , 10.1109/TSMCB.2012.2195723
Maryam Saadvandi, Karl Meerbergen, Wim Desmet, Parametric dominant pole algorithm for parametric model order reduction Journal of Computational and Applied Mathematics. ,vol. 259, pp. 259- 280 ,(2014) , 10.1016/J.CAM.2013.09.012
Minhui Sun, James Lam, Shengyuan Xu, Zhan Shu, Optimal time-weighted H 2 model reduction for Markovian jump systems International Journal of Control. ,vol. 85, pp. 613- 628 ,(2012) , 10.1080/00207179.2012.661081
F. M. Al-Sunni, F. L. Lewis, Optimal output tracker using a time‐weighted performance index Optimal Control Applications & Methods. ,vol. 19, pp. 55- 62 ,(1998) , 10.1002/(SICI)1099-1514(199801/02)19:1<55::AID-OCA611>3.0.CO;2-5
P. Bolzern, P. Colaneri, G. De Nicolao, Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching IEEE Transactions on Automatic Control. ,vol. 58, pp. 209- 213 ,(2013) , 10.1109/TAC.2012.2203049
Junling Wang, James Lam, Shengyuan Xu, Zhan Shu, Time-Multiplied Guaranteed Cost Control of Linear Delay Systems Journal of Dynamic Systems Measurement and Control-transactions of The Asme. ,vol. 130, pp. 061007- ,(2008) , 10.1115/1.2977473