LMI-based robust admissible control for uncertain singular delta operator systems

References

• Chadli, M., & Darouach, M. (2012). Novel bounded real lemma for discrete-time descriptor systems: Application to H∞ control design. Automatica, 48, 449–453.
   Web of Science ®Google Scholar
• Chen, S., & Shiau, L. (2011). Robust stability of uncertain singular time-delay systems via LFT approach. International Journal of Systems Science, 42, 31–39.
   Web of Science ®Google Scholar
• Dai, L. (1989). Singular control systems. Berlin: Springer-Verlag.
   Google Scholar
• Dong, X. (2007). Robust strictly dissipative control for discrete singular systems. IET Control Theory and Applications, 1(4), 1060–1067.
   Web of Science ®Google Scholar
• Dong, X. (2012). Controllability analysis of linear singular delta operator systems. In 12th International Conference on Control, Automation, Robotics and Vision (pp. 1199–1204). New York, NY: IEEE.
   Google Scholar
• Dong, X. (in press). Admissibility analysis of linear singular systems via a delta operator method. International Journal of Systems Science. doi: 10.1080/00207721.2013.769646.
   Google Scholar
• Dong, X., Mao, Q., Tian, W., & Wang, D. (2013). Observability analysis of linear singular delta operator systems. In 10th IEEE International Conference on Control and Automation (pp. 10–15). New York, NY: IEEE.
   Google Scholar
• Dong, X., Tian, W., Mao, Q., & Wang, D. (2013). Robust admissibility analysis and synthesis of uncertain singular systems via delta operator approach. In 10th IEEE International Conference on Control and Automation (pp. 1059–1064). New York, NY: IEEE.
   Google Scholar
• Goodwin, G.C., Leal, R.L., Mayne, D.Q., & Middleton, R.H. (1986). Rapproachement between continuous and discrete model reference adaptive control. Automatica, 22(2), 199–207.
   Web of Science ®Google Scholar
• Hsiung, K.L., & Lee, L. (1999). Lyapunov inequality and bounded real lemma for discrete-time descriptor systems. IEE Proceedings – Control Theory and Applications, 146(4), 327–331.
   Google Scholar
• Huang, C. (2013). Stability analysis and controller synthesis for fuzzy descriptor systems. International Journal of Systems Science, 44(1), 23–33.
   Web of Science ®Google Scholar
• Kumar, A., & Daoutidis, P. (1995). Feedback control of nonlinear differential-algebraic equation systems. AIChE Journal, 41, 619–636.
   Web of Science ®Google Scholar
• Lee, L., & Chen, J.L. (2003). Strictly positive real lemma and absolute stability for discrete-time descriptor systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50(6), 788–794.
   Google Scholar
• Li, H., Wu, B., Li, G., & Yang, C. (2005). Basic theory of delta operator control and robust control. Beijing: National Defence Industry Press.
   Google Scholar
• Luenberger, D.G., & Arbel, A. (1977). Singular dynamical Leotief systems. Econometrica, 5, 991–995.
   Google Scholar
• Mao, Q., Dong, X., & Tian, W. (2012). Admissibility conditions for linear singular delta operator systems: Analysis and synthesis. In 2012 World Congress on Intelligent Control and Automation (pp. 1870–1875). New York, NY: IEEE.
   Google Scholar
• Masubuchi, I. (2006). Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains. Systems and Control Letters, 55(2), 158–164.
   Web of Science ®Google Scholar
• Middleton, R., & Goodwin, G.C. (1986). Improved finite word length characteristics in digital control using delta operators. IEEE Transactions on Automatic Control, 31(11), 1015–1021.
   Web of Science ®Google Scholar
• Newcomb, R.W. (1981). The semistate description of nonlinear time variable circuits. IEEE Transactions on Circuits and Systems, 28, 62–67.
   Google Scholar
• Qiu, J., Xia, Y., Yang, H., & Zhang, J. (2008). Robust stabilization for a class of discrete-time systems with time-varying delays via delta operators. IET Control Theory and Applications, 2(1), 87–93.
   Web of Science ®Google Scholar
• Ren, J., & Zhang, Q. (2013). Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback. International Journal of Systems Science, 44(3), 450–460.
   Web of Science ®Google Scholar
• Wang, R., Xing, J., Wang, P., & Yang, Q. (2012). Non-fragile observer design for nonlinear switched time delay systems using delta operator. In 2012 UKACC International Conference on Control (pp. 387–393). New York, NY: IEEE.
   Google Scholar
• Wu, J., Li, G., Istepanian, R.H., & Chu, J. (2000). Shift and delta operator realisation for digital controllers with finite word length consideration. IEE Proceedings – Control Theory and Applications, 147(6), 664–672.
   Google Scholar
• Wu, Z., Shi, P., Su, H., & Chu, J. (2012). Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay. International Journal of Systems Science, 43(11), 2095–2106.
   Web of Science ®Google Scholar
• Xiang, Z., & Wang, R. (2010). Robust H∞ control for a class of uncertain switched systems using delta operator. Transactions of the Institute of Measurement and Control, 32(3), 331–344.
   Web of Science ®Google Scholar
• Xing, J., Wang, R., Wang, P., & Yang, Q. (2012). Robust control for a class of uncertain switched time delay systems using delta operator. In 12th International Conference on Control, Automation, Robotics and Vision (pp. 518–523). New York, NY: IEEE.
   Google Scholar
• Xu, S., & Lam, J. (2004a). New positive realness conditions for uncertain discrete descriptor systems: Analysis and synthesis. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(9), 1897–1902.
   Web of Science ®Google Scholar
• Xu, S., & Lam, J. (2004b). Robust stability and stabilization of discrete singular systems: An equivalent characterization. IEEE Transactions on Automatic Control, 49(4), 568–574.
   Web of Science ®Google Scholar
• Xu, S., & Yang, C. (1999). Stabilization of discrete-time singular systems: A matrix inequalities approach. Automatica, 35, 1613–1617.
   Web of Science ®Google Scholar
• Xu, S., Yang, C., Niu, Y., & Lam, J. (2001). Robust stabilization for uncertain discrete singular systems. Automatica, 37, 769–774.
   Web of Science ®Google Scholar
• Yang, H., & Xia, Y. (2012). Low frequency positive real control for delta operator systems. Automatica, 48(8), 1791–1795.
   Web of Science ®Google Scholar
• Yang, H., Xia, Y., & Shi, P. (2010). Observer-based sliding mode control for a class of discrete systems via delta operator approach. Journal of The Franklin Institute, 347(5), 1199–1213.
   Web of Science ®Google Scholar
• Yang, H., Xia, Y., Shi, P., & Fu, M. (2011). A novel delta operator Kalman filter design and convergence analysis. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(10), 2458–2468.
   Web of Science ®Google Scholar
• Yang, H., Xia, Y., Shi, P., & Fu, M. (2012). Stability analysis for high frequency networked control systems. IEEE Transactions on Automatic Control, 57(10), 2694–2700.
   Web of Science ®Google Scholar
• Yang, H., Xia, Y., Shi, P., & Zhao, L. (2012). Analysis and synthesis of delta operator systems. Berlin: Springer-Verlag.
   Google Scholar
• Zhang, G., Xia, Y., & Shi, P. (2008). New bounded real lemma for discrete-time singular systems. Automatica, 44, 886–890.
   Web of Science ®Google Scholar