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Linked References

1. V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol. 22, no. 2, pp. 212–222, 1977. View at Zentralblatt MATH · View at MathSciNet
2. V. I. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering Series, Springer, Berlin, Germany, 1992. View at MathSciNet
3. Y. Xia, Z. Zhu, C. Li, H. Yang, and Q. Zhu, “Robust adaptive sliding mode control for uncertain discrete-time systems with time delay,” Journal of the Franklin Institute, vol. 347, no. 1, pp. 339–357, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
4. H. H. Choi, “LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems,” IEEE Transactions on Automatic Control, vol. 52, no. 4, pp. 736–742, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
5. X. R. Han, E. Fridman, S. K. Spurgeon, and C. Edwards, “On the design of sliding-mode static-output-feedback controllers for systems with state delay,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3656–3664, 2009. View at Publisher · View at Google Scholar
6. H. Yang, Y. Xia, and P. Shi, “Observer-based sliding mode control for a class of discrete systems via delta operator approach,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1199–1213, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. E. Fridman, F. Gouaisbaut, M. Dambrine, and J.-P. Richard, “Sliding mode control of systems with time-varying delays via desciptor approach,” International Journal of Systems Science, vol. 34, no. 8-9, pp. 553–559, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
8. Y. Xia and Y. Jia, “Robust sliding-mode control for uncertain time-delay systems: an LMI approach,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 1086–1092, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
9. C.-C. Wen and C.-C. Cheng, “Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability,” Journal of the Franklin Institute, vol. 345, no. 8, pp. 926–941, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
10. Y. Niu, D. W. C. Ho, and X. Wang, “Robust $H_{\infty }$ control for nonlinear stochastic systems: a sliding-mode approach,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1695–1701, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
11. H. Wang, Z.-Z. Han, Q.-Y. Xie, and W. Zhang, “Sliding mode control for chaotic systems based on LMI,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1410–1417, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
12. N. Cai, Y. Jing, and S. Zhang, “Modified projective synchronization of chaotic systems with disturbances via active sliding mode control,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1613–1620, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
13. Y. Niu, D. W. C. Ho, and X. Wang, “Sliding mode control for Itô stochastic systems with Markovian switching,” Automatica, vol. 43, no. 10, pp. 1784–1790, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. L. Wu, X. Yao, and W. X. Zheng, “Generalized $H_2$ fault detection for two-dimensional Markovian jump systems,” Automatica, vol. 48, no. 8, pp. 1741–1750, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
15. W. Xiang and F. Chen, “An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 1–9, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
16. E. K. Boukas, S. Xu, and J. Lam, “On stability and stabilizability of singular stochastic systems with delays,” Journal of Optimization Theory and Applications, vol. 127, no. 2, pp. 249–262, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. Z. Wu, H. Su, J. Chu, and W. Zhou, “Improved result on stability analysis of discrete stochastic neural networks with time delay,” Physics Letters A, vol. 373, no. 17, pp. 1546–1552, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
18. Y. Xia, E.-K. Boukas, P. Shi, and J. Zhang, “Stability and stabilization of continuous-time singular hybrid systems,” Automatica, vol. 45, no. 6, pp. 1504–1509, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
19. S. Wo, Y. Zou, M. Sheng, and S. Xu, “Robust control for discrete-time singular large-scale systems with parameter uncertainty,” Journal of the Franklin Institute, vol. 344, no. 2, pp. 97–106, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
20. J. Raouf and E. K. Boukas, “Stochastic output feedback controller for singular Markovian jump systems with discontinuities,” IET Control Theory & Applications, vol. 3, no. 1, pp. 68–78, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
21. J. H. Kim, “New design method on memoryless $H_{\infty }$ control for singular systems with delayed state and control using LMI,” Journal of the Franklin Institute, vol. 342, no. 3, pp. 321–327, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. S. Ma, C. Zhang, and Z. Cheng, “Delay-dependent robust $H_{\infty }$ control for uncertain discrete-time singular systems with time-delays,” Journal of Computational and Applied Mathematics, vol. 217, no. 1, pp. 194–211, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. S. Zhou and W. X. Zheng, “Robust $H_{\infty }$ control of delayed singular systems with linear fractional parametric uncertainties,” Journal of the Franklin Institute, vol. 346, no. 2, pp. 147–158, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
24. W. Zhou and J. Fang, “Delay-dependent robust $H_{\infty }$ admissibility and stabilization for uncertain singular system with Markovian jumping parameters,” Circuits, Systems, and Signal Processing, vol. 28, no. 3, pp. 433–450, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
25. N. Kumaresan and P. Balasubramaniam, “Optimal control for stochastic nonlinear singular system using neural networks,” Computers & Mathematics with Applications, vol. 56, no. 9, pp. 2145–2154, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
26. S. Ma and E. K. Boukas, “Robust $H_{\infty }$ filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay,” IET Control Theory & Applications, vol. 3, no. 3, pp. 351–361, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
27. S. Xu, J. Lam, and Y. Zou, “$H_{\infty }$ filtering for singular systems,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2217–2222, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
28. 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. View at Publisher · View at Google Scholar · View at MathSciNet
29. Y.-G. Kao, J.-F. Guo, C.-H. Wang, and X.-Q. Sun, “Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays,” Journal of the Franklin Institute, vol. 349, no. 6, pp. 1972–1988, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
30. L. Zhang and J. Lam, “Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1695–1701, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
31. L. Zhang and E.-K. Boukas, “Mode-dependent $H_{\infty }$ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 6, pp. 1462–1467, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
32. L. Zhang, “$H_{\infty }$ estimation for discrete-time piecewise homogeneous Markov jump linear systems,” Automatica, vol. 45, no. 11, pp. 2570–2576, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
33. L. Zhang, E.-K. Boukas, and J. Lam, “Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities,” IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2458–2464, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
34. L. Wu and D. W. C. Ho, “Sliding mode control of singular stochastic hybrid systems,” Automatica, vol. 46, no. 4, pp. 779–783, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
35. K. Gu, “A further refinement of discretized Lyapunov functional method for the stability of time-delay systems,” International Journal of Control, vol. 74, no. 10, pp. 967–976, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
36. E.-K. Boukas, Control of Singular Systems with Random Abrupt Changes, Communications and Control Engineering Series, Springer, Berlin, Germany, 2008. View at MathSciNet
37. D. Yue and Q.-L. Han, “Robust $H_{\infty }$ filter design of uncertain descriptor systems with discrete and distributed delays,” IEEE Transactions on Signal Processing, vol. 52, no. 11, pp. 3200–3212, 2004. View at Publisher · View at Google Scholar · View at MathSciNet