Abstract and Applied Analysis

Finite-Time H Control for Time-Delayed Stochastic Systems with Markovian Switching

Wenhua Gao, Feiqi Deng, Ruiqiu Zhang, and Wenhui Liu

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Abstract

This paper studies the problem of finite-time H control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-time H control is obtained. Simulation results illustrate the effectiveness of the proposed method.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 809290, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273178

Digital Object Identifier
doi:10.1155/2014/809290

Mathematical Reviews number (MathSciNet)
MR3173292

Zentralblatt MATH identifier
07023118

Citation

Gao, Wenhua; Deng, Feiqi; Zhang, Ruiqiu; Liu, Wenhui. Finite-Time ${H}_{\infty }$ Control for Time-Delayed Stochastic Systems with Markovian Switching. Abstr. Appl. Anal. 2014 (2014), Article ID 809290, 10 pages. doi:10.1155/2014/809290. https://projecteuclid.org/euclid.aaa/1412273178


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References

  • S. He and F. Liu, “Finite-time ${H}_{\infty }$ filtering of time-delay stochastic jump systems with unbiased estimation,” Proceedings of the Institution of Mechanical Engineers, vol. 224, no. 8, pp. 947–959, 2010.
  • S. B. Stojanović, D. Lj. Debeljković, and D. S. Antić, “Finite-time stability and stabilization of linear time-delay systems,” Facta Universitatis, vol. 11, no. 1, pp. 25–36, 2012.
  • Z. Xiang, Y.-N. Sun, and M. S. Mahmoud, “Robust finite-time ${H}_{\infty }$ control for a class of uncertain switched neutral systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1766–1778, 2012.
  • P. Dorato, “Short-time stability in linear time-varying systems,” IRE International Convention Record, pp. 83–87, 1961.
  • P. Dorato, “Short-time stability,” IRE Transactions on Automatic Control, pp. 6–86, 1961.
  • L. Weiss and E. F. Infante, “Finite time stability under perturbing forces and on product spaces,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 12, pp. 54–59, 1967.
  • A. N. Michel and S. H. Wu, “Stability of discrete systems over a finite interval of time,” International Journal of Control, vol. 9, pp. 679–693, 1969.
  • H. J. Kushner, “Finite time stochastic stability and the analysis of tracking systems,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 11, pp. 219–227, 1966.
  • H. J. Kushner, Stochastic Stability and Control, vol. 33 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1967.
  • W. L. Garrard, “Further results on the synthesis of finite-time stable systems,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 17, pp. 142–144, 1972.
  • L. Van Mellaert and P. Dorato, “Numerical solution of an optimal control problem with a probability criterion,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 543–546, 1972.
  • L. Van Mellaert, Inclusion-probability-optimal control [Ph.D. thesis], Polytechnic Institute of Brooklyn, 1967.
  • F. A. San Filippo and P. Dorato, “Short-time parameter optimization with flight control application,” Automatica, vol. 10, no. 4, pp. 425–430, 1974.
  • P. Dorato, C. T. Abdallah, and D. Famularo, “Robust finite-time stability design via linear matrix inequalities,” in Proceedings of the 36th IEEE Conference on Decision and Control, pp. 1305–1306, San Diego, Calif, USA, December 1997.
  • F. Amato, M. Ariola, and P. Dorato, “Finite-time control of linear systems subject to parametric uncertainties and disturbances,” Automatica, vol. 37, no. 9, pp. 1459–1463, 2001.
  • F. Amato and M. Ariola, “Finite-time control of discrete-time linear systems,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 50, no. 5, pp. 724–729, 2005.
  • F. Amato, M. Ariola, and C. Cosentino, “Finite-time stabilization via dynamic output feedback,” Automatica, vol. 42, no. 2, pp. 337–342, 2006.
  • S. Xing, Q. Zhang, and Y. Zhang, “Finite-time stability analysis and control for a class of stochastic singular biological economic systems based on T-S fuzzy model,” Abstract and Applied Analysis, vol. 2013, Article ID 946491, 10 pages, 2013.
  • R. Wang, J. Xing, P. Wang, Q. Yang, and Z. Xiang, “${H}_{\infty }$ control with finite-time stability for switched systems under asynchronous switching,” Mathematical Problems in Engineering, vol. 2012, Article ID 929503, 16 pages, 2012.
  • L. Hou, G. Zong, and Y. Wu, “Finite-time control for switched delay systems via dynamic output feedback,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 7A, pp. 4901–4913, 2012.
  • W. H. Zhang and X. Y. An, “Finite-time control of linear stochastic systems,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 3, pp. 687–694, 2008.
  • J. Zhou, S. Xu, and H. Shen, “Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks,” Neurocomputing, vol. 74, no. 17, pp. 2790–2796, 2011.
  • Z. Yan, G. Zhang, and J. Wang, “Finite-time stability and stabilization of linear stochastic systems,” in Proceedings of the 29th Chinese Control Conference (CCC '10), pp. 1115–1120, Beijing, China, July 2010.
  • Z. Yan, G. Zhang, and J. Wang, “Finite-time guaranteed cost control for linear stochastic systems,” in Proceedings of the 30th Chinese Control Conference (CCC '11), pp. 1389–1394, Yantai, China, July 2011.
  • A. N. Michel and L. Hou, “Finite-time and practical stability of a class of stochastic dynamical systems,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 3452–3456, Cancun, Mexico, December 2008.
  • Y. Yang, J. Li, and G. Chen, “Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects,” Journal of Systems Engineering and Electronics, vol. 21, no. 2, pp. 254–260, 2010.
  • Y. Yang, J. Li, and G. Chen, “Finite-time stability and stabilization of nonlinear stochastic hybrid systems,” Journal of Mathematical Analysis and Applications, vol. 356, no. 1, pp. 338–345, 2009.
  • H. Ma and Y. Jia, “Input-output finite-time stability and stabilization of stochastic Markovian jump systems,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC '11), Orlando, Fla, USA, December 2011.
  • S. He and F. Liu, “Observer-based finite-time control of time-delayed jump systems,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2327–2338, 2010.
  • Z. Zuo, H. Li, Y. Liu, and Y. Wang, “On finite-time stochastic stability and stabilization of markovian jump systems subject to partial information on transition probabilities,” Circuits, Systems and Signal Processing, vol. 31, no. 6, pp. 1973–1983, 2012.
  • Y. Zhang, C. Liu, and X. Mu, “Robust finite-time stabilization of uncertain singular Markovian jump systems,” Applied Mathematical Modelling, vol. 36, no. 10, pp. 5109–5121, 2012.
  • Y. Sun and J. Xu, “Finite-time boundedness and stabilization of networked control systems with time delay,” Mathematical Problems in Engineering, vol. 2012, Article ID 705828, 12 pages, 2012.
  • X. Zhang, H. Zhang, X. Wang, and Y. Luo, “A new iteration approach to solve a class of finite-horizon continuous-time nonaffine nonlinear zero-sum game,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 2, pp. 597–608, 2011.
  • H. Liu, Y. Shen, and X. Zhao, “Delay-dependent observer-based ${H}_{\infty }$ finite-time control for switched systems with time-varying delay,” Nonlinear Analysis: Hybrid Systems, vol. 6, no. 3, pp. 885–898, 2012.
  • H. Song, L. Yu, D. Zhang, and W.-A. Zhang, “Finite-time ${H}_{\infty }$ control for a class of discrete-time switched time-delay systems with quantized feedback,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4802–4814, 2012.
  • Z. Xiang, C. Qiao, and M. S. Mahmoud, “Finite-time analysis and ${H}_{\infty }$ control for switched stochastic systems,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 915–927, 2012.
  • Y. Zhang, W. Cheng, X. Mu, and X. Guo, “Observer-based finite-time ${H}_{\infty }$ control of singular Markovian jump systems,” Journal of Applied Mathematics, vol. 2012, Article ID 205727, 19 pages, 2012.
  • Y. Zhang, C. Liu, and X. Mu, “Robust finite-time ${H}_{\infty }$ control of singular stochastic systems via static output feedback,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5629–5640, 2012.
  • Y. Zhang, W. Cheng, X. Mu, and C. Liu, “Stochastic ${H}_{\infty }$ finite-time control of discrete-time systems with packet loss,” Mathematical Problems in Engineering, vol. 2012, Article ID 897481, 15 pages, 2012.
  • Y. Wang, P. Shi, Q. Wang, and D. Duan, “Exponential ${H}_{\infty }$ filtering for singular Markovian jump systems with mixed mode-dependent time-varying delay,” IEEE Transactions on Circuits and Systems, vol. 60, no. 9, pp. 2440–2452, 2013.
  • F. Li, X. Wang, and P. Shi, “Robust quantized ${H}_{\infty }$ control for networked control systems with Markovian jumps and time delays,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 12, pp. 4889–4902, 2013.
  • L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded ${l}_{2}$ gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012.
  • P. Shi and M. Liu, “Discussion on: `On the filtering problem for continuous-time Markov jump linear systems with no observation of the Markov chain',” European Journal of Control, vol. 17, no. 4, pp. 355–356, 2011.
  • M. Liu, P. Shi, L. Zhang, and X. Zhao, “Fault-tolerant control for nonlinear Markovian jump systems via proportional and derivative sliding mode observer technique,” IEEE Transactions on Circuits and Systems, vol. 58, no. 11, pp. 2755–2764, 2011.
  • P. Shi, Y. Xia, G. P. Liu, and D. Rees, “On designing of sliding-mode control for stochastic jump systems,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 51, no. 1, pp. 97–103, 2006.
  • S. He and F. Liu, “Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 2631–2638, 2011.
  • W. Gao and F. Deng, “Delay-dependent exponential stability of uncertain stochastic systems with discrete and distributed delays,” Dynamics of Continuous, Discrete & Impulsive Systems B, vol. 16, no. 5, pp. 617–629, 2009.
  • X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK, 1997.
  • H. Liu and Y. Shen, “${H}_{\infty }$ finite-time control for switched linear systems with time-varying delay,” Interlligent Control and Automation, vol. 2, no. 2, pp. 203–213, 2011. \endinput