Robust H∞ control for uncertain Markovian jump systems with mixed delays

doi:10.1088/1674-1056/25/7/070201

中国物理B ›› 2016, Vol. 25 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/25/7/070201

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Robust H_∞ control for uncertain Markovian jump systems with mixed delays

R Saravanakumar, M Syed Ali

Department of Mathematics, Thiruvalluvar University, Vellore-632115, Tamil Nadu, India

收稿日期:2015-09-11 修回日期:2016-03-21 出版日期:2016-07-05 发布日期:2016-07-05
通讯作者: R Saravanakumar, M Syed Ali E-mail:saravanamaths30@gmail.com;syedgru@gmail.com
基金资助:
Project supported by Department of Science and Technology (DST) under research project No. SR/FTP/MS-039/2011.

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

R Saravanakumar, M Syed Ali

Department of Mathematics, Thiruvalluvar University, Vellore-632115, Tamil Nadu, India

Received:2015-09-11 Revised:2016-03-21 Online:2016-07-05 Published:2016-07-05
Contact: R Saravanakumar, M Syed Ali E-mail:saravanamaths30@gmail.com;syedgru@gmail.com
Supported by:
Project supported by Department of Science and Technology (DST) under research project No. SR/FTP/MS-039/2011.

摘要/Abstract

摘要： We scrutinize the problem of robust H_∞ control for a class of Markovian jump uncertain systems with interval time-varying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H_∞ control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H_∞ control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

关键词: linear matrix inequality, Lyapunov method, Markovian jumping parameters, robust H_∞ control

Abstract: We scrutinize the problem of robust H_∞ control for a class of Markovian jump uncertain systems with interval time-varying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H_∞ control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H_∞ control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

Key words: linear matrix inequality, Lyapunov method, Markovian jumping parameters, robust H_∞ control

中图分类号: (Matrix theory)

02.10.Yn

02.30.Hq (Ordinary differential equations) 02.30.Ks (Delay and functional equations) 02.30.Yy (Control theory)

R Saravanakumar, M Syed Ali. Robust H_∞ control for uncertain Markovian jump systems with mixed delays[J]. 中国物理B, 2016, 25(7): 70201-070201.

R Saravanakumar, M Syed Ali. Robust H_∞ control for uncertain Markovian jump systems with mixed delays[J]. Chin. Phys. B, 2016, 25(7): 70201-070201.

参考文献 20

[1]	Syed Ali M and Saravanakumar R 2015 Chin. Phys. B 24 050201
[2]	Syed Ali M and Saravanakumar R 2015 Chin. Phys. B 24 090202
[3]	Kwon O M, Park J H and Lee S M 2010 J. Optim. Theory Appl. 145 343
[4]	Arunkumar A, Sakthivel R and Mathiyalagan K 2015 Neurocomputing 149 1524
[5]	Lei T, Song Q and Zhao Z 2014 Discrete Dyn. Nat. Soc. 2014 657621
[6]	Xu S, Lam J and Yang C 2001 IEEE Trans. Automat. Control 46 1321
[7]	Jeong C, Park P G and Kim S H 2012 Appl. Math. Comput. 218 10533
[8]	Lee W I, Lee S Y and Park P G 2014 Appl. Math. Comput. 243 570
[9]	Zhao X and Zeng Q 2010 J. Frankl. Inst. 347 863
[10]	Liu J, Yao B and Gu Z 2011 Circuit Syst. Signal Process. 30 1253
[11]	Karimi H R 2012 J. Franklin Inst. 349 1480
[12]	Syed Ali M, Arik S and Saravanakmuar R 2015 Neurocomputing 158 167
[13]	Lien C H, Chen J D, Yu K W and Chung L Y 2012 Comput. Math. Appl. 64 1187
[14]	Wang C and Shen Y 2012 Comput. Math. Appl. 63 985
[15]	Senthilkumar T and Balasubramaniam P 2011 Appl. Math. Lett. 24 1986
[16]	Syed Ali M and Saravanakumar R 2014 Chin. Phys. B 23 120201
[17]	Syed Ali M and Saravanakumar R 2014 Appl. Math. Comput. 249 510
[18]	Gu K, Kharitonov V L and Chen J 2003 Stability of Time-Delay Systems (Boston: Birkhuser)
[19]	Chen B, Liu X and Lin C 2009 Fuzzy Sets and Systems 160 403
[20]	Xu D, Li B, Long S and Teng L 2014 Nonlinear Anal. 108 128

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

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