Abstract
This paper deals with the problem of robust normalization and delay-dependent H ∞ control for a class of singular Markovian jump systems with norm-bounded parameter uncertainties and time delay. A new impulsive and proportional-derivative control strategy with memory is presented, which results in a novel class of hybrid impulsive systems. Sufficient conditions are developed to guarantee that the resultant closed-loop system is not only robust normal and stochastically stable, but also satisfies a prescribed H ∞ performance level for all delays no larger than a given upper bound. In addition, the explicit expression of the desired impulsive control gains is also given together with the design approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
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J. R. Wang, H. Wang, A. K. Xue, and R. Q. Lu, “Delaydependent H ∞ control for singular Markovian jump systems with time delay,” Nonlinear Analysis: Hybrid Systems, vol. 8, pp. 1–12, 2013. [click]
G. L. Wang, “Robust stabilization of singular Markovian jump systems with uncertain switching,” International Journal of Control, Automation and Systems, vol. 11, no. 1, pp. 188–193, 2013. [click]
P. Shi and F. B. Li, “A survey on Markovian jump systems: Modeling and design,” International Journal of Control, Automation and Systems, vol. 13, no. 1, pp. 1–16, 2015.
W. L. Li and Y. M. Jia, “Rao-Blackwellised unscented particle ltering for jump Markov non-linear systems: an H ∞ approach,” IET Signal Processing, vol. 5, no. 2, pp. 187–193, 2011. [click]
W. L. Li and Y. M. Jia, “Rao-Blackwellised particle ltering and smoothing for jump Markov non-linear systems with mode observation,” IET Signal Processing, vol. 7, no. 4, pp. 327–336, 2013. [click]
M. Q. Shen and D. Ye, “Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions,” Fuzzy Sets and Systems, vol. 217, pp. 80–95, 2013. [click]
J. X. Dong and G. H. Yang, “Robust H2 control of continuous-time Markov jump linear systems,” Automatica, vol. 44, no. 5, pp. 1431–1436, 2008. [click]
Z. G. Wu, P. Shi, H. Y. Su, and J. Chu, “Asynchronous l2 H ∞ ltering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities,” Automatica, vol. 50, no. 1, pp. 180–186, 2014. [click]
T. H. Lee, Q. Ma, S. Xu, and J. H. Park, “Pinning control for cluster synchronisation of complex dynamical networks with semi-Markovian jump topology,” International Journal of Control, vol. 88, no. 6, pp. 1223–1235, 2015.
T. H. Lee, J. H. Park, S. M. Lee, and O. M. Kwon, “Robust sampled-data control with random missing data scenario,” International Journal of Control, vol. 87, no.9, pp. 1957–1969, 2014. [click]
Y. Y. Cao and J. Lam, “Robust H ∞ control of uncertain Markovian jump systems with time-delay,” IEEE Trans. on Automatic Control, vol. 45, no. 1, pp. 77–83, 2000. [click]
Z. Wang, J. Lam, and X. Liu, “Exponential ltering for uncertainMarkovian jump time-delay systems with nonlinear disturbances,” IEEE Trans. on Circuits and Systems II: Express Briefs, vol. 51, no. 5, pp. 262–268, 2004. [click]
N. Chaibi and E. H. Tissir, “Delay dependent robust stability of singular systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 10, no. 3, pp. 632–638, 2012. [click]
T. H. Lee, M. J. Park, J. H. Park and O. M. Kwon, “Extended dissipative analysis for neural networks with timevarying delays,” IEEE Trans. on Neural Networks and Learning Systems, vol. 25, no. 10, pp. 1936–1941, 2014. [click]
Z. G. Wu, P. Shi, H. Y. Su, and J. Chu, “Stochastic synchronization of Markovian jump neural networks with timevarying delay using sampled-data,” IEEE Trans. on Cybernetics, vol. 43, no. 6, pp. 1796–1806, 2013. [click]
J. Wu, T. Chen, and L. Wang, “Delay-dependent robust stability and H ∞ control for jump linear systems with delays,” Systems & Control Letters, vol. 55, no. 11, pp. 939–948, 2006. [click]
H. Zhang, Z. H. Guan, and G. Feng, “Reliable dissipative control for stochastic impulsive systems,” Automatica, vol. 44, no. 4, pp. 1004–1010, 2008. [click]
B. Li, D. Li, and D. Xu, “Stability analysis for impulsive stochastic delay differential equations with Markovian switching,” Journal of the Franklin Institute, vol. 350, no. 7, pp. 1848–1864, 2013. [click]
D. Yue, J. Lam, and D. W. C. Ho, “Reliable H ∞ control of uncertain descriptor systems with multiple time delays,” IEEProceedings of Control Theory and Applications, vol. 150, no. 6, pp. 557–564, 2003. [click]
Q. L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, vol. 41, no. 12, pp. 2171–2176, 2005. [click]
L. Huang, Linear Algebra in System and Control Theory, Science Publish House, Beijing, 1984.
I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems & Control Letters, vol. 8, no. 4, pp. 351–357, 1987. [click]
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Recommended by Associate Editor Yingmin Jia under the direction of Editor PooGyeon Park. This work was supported by the National Natural Science Foundation of China under Grants 61273008 and 61203001.
Hui Lv received her B.S. and M.S. degrees in applied mathematics from Liaoning University, Shenyang, China, in 2004 and 2009, respectively. She is pursuing a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China. Her research interests include singular Markovian systems and impulsive control.
Qingling Zhang received the B.S. and M.S. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986 and 1995, respectively. Dr. Zhang is now a Professor at Institute of Systems Science, Northeastern University. His research interests include singular systems and stochastic systems.
Junchao Ren received his B.S. degree in applied mathematics from Northeastern University, Shenyang, China, in 2000 and an M.S. degree in control theory and control engineering from Guangdong University of Technology, Guangzhou, in 2003 and a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2011. Dr. Ren is currently an associate professor with Institute of Systems Science, Northeastern University, Shenyang, China. His research interests include robust control and singular systems.
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Lv, H., Zhang, Q. & Ren, J. Delay-dependent H ∞ control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control. Int. J. Control Autom. Syst. 14, 939–947 (2016). https://doi.org/10.1007/s12555-015-0097-9
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DOI: https://doi.org/10.1007/s12555-015-0097-9