A probabilistic solution of robust H_∞ control problem with scaled matrices

References

• Alamo, T., & Tempo, R. (2009). Randomized strategies for probabilistic solutions of uncertain feasibility and optimization problems. IEEE Transactions on Automatic Control, 54(11), 2545–2558.
   Web of Science ®Google Scholar
• Apkarian, P., & Gahinet, P. (1995). A convex characterization of gain-scheduled H∞ controllers. IEEE Transactions on Automatic Control, 40, 853–864.
   Web of Science ®Google Scholar
• Bai, E.W., Tempo, R., & Fu, M. (1998). Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis. Mathematics of Control, Signals, and Systems, 11(3), 183–196.
   Web of Science ®Google Scholar
• Balas, G.J., Doyle, J.C., Glover K., Packard, A., & Smith, R. (1991). μ-Analysis and synthesis toolbox. Natick, MA: Mathworks.
   Google Scholar
• Barmish, B.R., Lagoa, C.M., & Tempo, R. (1997). Radially truncated uniform distributions for probabilistic robustness of control systems. In Proceedings of American Control Conference (pp. 853–857). Albuquerque, NM.
   Google Scholar
• Boyd, S., & Vandenberghe, L. (2004). Convex optimization (pp. 561–596). Cambridge: Cambridge University Press.
   Google Scholar
• Calafiore, G., Dabbene, F., & Tempo, R. (2011). Research on probabilistic method for control the system design. Automatica, 47(2), 1279–1293.
   Web of Science ®Google Scholar
• Chen, X., Zhou, K.& Aravena, J. (2009). A new statistical approach for the analysis of uncertain systems. Journal of Systems Science and Complexity, 22(1), 1–34.
   Web of Science ®Google Scholar
• Dinh, Q.T., Gumussoy, S., Michiels, W., & Diehl, M. (2012). Combining convex-concave decompositions and linearization approaches for solving BMIs, with application to static output feedback. IEEE Transactions on Automatic Control, 57(6), 1377–1389.
   Web of Science ®Google Scholar
• Fukuda, M., & Kojima, M. (2001). Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. Computational Optimization and Applications, 19, 79–105.
   Web of Science ®Google Scholar
• Gahinet, P., & Apkarian, P. (1994). A linear matrix inequality approach to H∞ control. International Journal of Robust and Nonlinear Control, 4(4), 421–448.
   Web of Science ®Google Scholar
• Goh, K.C., Safonov, M.G., & Papavassilopoulos, G.P. (1994). A global optimization approach for the BMI problem. In Proceedings of the IEEE Conference on Decision Control (pp. 2009–2014). Lake Buena Vista, FL.
   Google Scholar
• Jaulin, L., & Henrion, D. (2005). Contracting optimally an interval matrix without loosing any positive semi-definite matrix is a tractable problem. Reliable Computing, 11(1), 1–17.
   Google Scholar
• Juradoa, I., Ortegaa, M.G., Quevedob, D.E., & Rubio, F.R. (2013). An H∞ suboptimal robust control approach for systems with uncertainties and data dropouts. International Journal of Systems Science. doi: 10.1080/00207721.2013.843733
   Google Scholar
• Kanev, S., Scherer, C., Verhaegen, M., & De Schutter, B. (2003). A BMI optimization approach to robust output-feedback control. In Proceedings of the 42nd IEEE Conference on Decision and Control (pp. 851–856). Maui, HI.
   Google Scholar
• Li, X., & Gao, H. (2014). A Heuristic approach to static output-feed-back controller synthesis with restricted frequency-domain specifications. IEEE Transactions on Automatic Control, 59(4), 1008–1014.
   Web of Science ®Google Scholar
• Packard, A.K., Zhou, K., Pandey, P., Leonhardson, J., & Balas, G. (1992). Optimal, constant I/O similarity scaling for full-information and state-feed back control problems. Systems and Control Letters, 19, 271–280.
   Web of Science ®Google Scholar
• Tempo, R., Calafiore, G.C., & Dabbene, F. (2013). Randomized algorithms for analysis and control of uncertain the system[M] (pp. 277–282). London: Springer Verlag.
   Google Scholar
• Tremba, A., Calafiore, G., Dabbene, F., Gryazina, E., Polyak, B., Shcherbakov, P., & Tempo, R. (2010). RACT: Randomized algorithms control toolbox for MATLAB. In Proceedings of the 17th International Federation of Automatic Control (pp. 390–395). Seoul.
   Google Scholar
• Tulpule, P., & Kelkar, A. (2013). BMI based robust optimal control synthesis via sensitivity minimization. In Proceedings of the 6th Annual Dynamic Systems and Control Conference (pp. 21–23). Palo Alto, CA.
   Google Scholar
• Wu, F., & Lu, B. (2004). On convexified robust control synthesis. Automatica, 40(6), 1003–1010.
   Web of Science ®Google Scholar
• Zhou, K., & Doyle, J.C. (1998). Essentials of robust control (pp. 233–246). London: Prentice Hall.
   Google Scholar