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Original Articles

An asymptotically exact LMI solution to the robust discretisation of LTI systems with polytopic uncertainties and its application to sampled-data control

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Pages 2702-2714 | Received 18 Mar 2013, Accepted 04 Jul 2013, Published online: 17 Jan 2014

References

  • Bamieh, B., Pearson, J., Francis, B., & Tannenbaum, A. (1991). A lifting technique for linear periodic systems. Systems and Control Letters, 17(2), 79–88.
  • Bhattacharyya, S.P., Chapellat, H., & Keel, L.H. (1995). Robust control: The parametric approach. Upper Saddle River, NJ: Prentice-Hall.
  • Boyarski, S. (2013). Polytopic best-mean H∞ performance analysis. International Journal of Systems Science, 44(7), 1193–1199.
  • Boyd, S., Ghaoui, L.El, Féron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in systems and control theory. Studies in Applied Mathematics. Philadelphia, PA: SIAM.
  • Chen, C.-T. (1995). Linear system theory and design. New York, NY: Oxford University Press.
  • Chen, T., & Francis, B.A. (1995). Optimal sampled-data control systems. London: Springer-Verlag.
  • Cuzzola, F.A., Geromel, J.C., & Morari, M. (2002). An improved approach for constrained robust model predictive control. Automatica, 38(7), 1183–1189.
  • de Oliveira, M.C., Bernussou, J., & Geromel, J.C. (1999). A new discrete-time robust stability condition. System and Control Letters, 37(4), 261–265.
  • de Oliveira, M.C., Geromel, J.C., & Bernussou, J. (2002). Extended H2 and H∞ norm characterizations and controller parameterizations for discrete-time systems. International Journal of Control, 75(9), 666–679.
  • Ding, B., Xi, Y., & Li, S. (2004). A synthesis approach of on-line constrained robust model predictive control. Automatica, 40(1), 163–167.
  • Ebihara, Y., Peaucelle, D., & Arzelier, D. (2011). Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems. Automatica, 47(1), 14–25.
  • Fridman, E. (2010). A refined input delay approach to sampled-data control. Automatica, 46(2), 421–427.
  • Fridman, E., Seuret, A., & Richard, J.-P. (2004). Robust sampled-data stabilization of linear systems: An input delay approach. Automatica, 40(8), 1441–1446.
  • Gahinet, P., Nemirovski, A., Laub, A.J., & Chilali, M. (1995). LMI control toolbox. Natick, MA: MathWorks.
  • Goncalves, E.N., Palhares, R.M., Takahashi, R.H.C., & Mesquita, R.C. (2007). New strategy for robust stability analysis of discrete-time uncertain systems. Systems and Control Letters, 56(7–8), 516–524.
  • Gu, K. (1994). H∞ control of systems under norm bounded uncertainties in all system matrices. IEEE Transactions on Automatic Control, 39(6), 1320–1322.
  • Hu, T., Lam, J., Cao, Y., & Shao, H. (2003). A LMI approach to robust H2 sampled-data control for linear uncertain systems. IEEE Transaction Systems Man and Cybernetics, 33(1), 149–155.
  • Iwasaki, T. (2011). Robust performance analysis for systems with structured uncertainty. International Journal of Robust and Nonlinear Control, 6(2), 95–99.
  • Kim, D.W., Lee, H.J., Park, J.B., & Joo, Y.H. (2006). Discretisation of continuous-time T–S fuzzy system: Global approach. IEE Proceedings of Control Theory and Applications, 153(2), 237–246.
  • Kim, D.W., Park, J.B., & Joo, Y.H. (2007). Effective digital implementation of fuzzy control systems based on approximate discrete-time models. Automatica, 43(10), 1671–1683.
  • Laila, D.S. (2003). Design and analysis of nonlinear sampled-data control systems (Ph.D. dissertation). Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne.
  • Lee, D.H., Park, J.B., Joo, Y.H., & Lin, K.C. (2011). Lifted versions of robust D-stability and D-stabilisation conditions for uncertain polytopic linear systems. IET Control Theory and Applications, 6(1), 24–36.
  • Li, D., Xi, Y., & Zheng, P. (2009). Constrained robust feedback model predictive control for uncertain systems with polytopic description. International Journal of Control, 82(7), 1267–1274.
  • Liu, Y.-Y., & Yang, G.-H. (2012). Sampled-data H∞ control for networked control systems with digital control inputs. International Journal of Systems Science, 43(9), 1728–1740.
  • Löfberg, J. (2004, September). YALMIP: A toolbox for modeling and optimization in MATLAB. IEEE International Symposium on Computer Aided Control Systems Design (pp. 284–289), Taipei.
  • Oliveira, R.C.L.F., de Oliveira, M.C., & Peres, P.L.D. (2008). Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions. Systems and Control Letters, 57(8), 680–689.
  • Oliveira, R.C.L.F., & Peres, P.L.D. (2005). Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions. Linear Algebra and its Applications, 405, 209–228.
  • Oliveira, R.C.L.F., & Peres, P.L.D. (2007). Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations. IEEE Transactions on Automatic Control, 52(7), 1334–1340.
  • Scherer, C.W. (2005). Relaxations for robust linear matrix inequality problems with verifications for exactness. SIAM Journal on Matrix Analysis and Applications, 27(2), 365–395.
  • Sivashankar, N., & Khargonekar, P. P. (1994). Characterization of the L2-induced norm for linear systems with jumps with application to sampled-data systems. SIAM Journal on Control and Optimization, 32(4), 1128–1150.
  • Strum, J.F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11–12, 625–653. http://sedumi.mcmaster.ca/
  • Yamamoto, Y. (1990). New approach to sampled-data control systems-a function space method. Proceedings of the 29th Conference on Decision and Control (pp. 1882–1887), Honolulu, HI.
  • Yang, G.-H., & Lum, K.-Y. (2007). Comparisons among robust stability criteria for linear systems with affine parameter uncertainties. Automatica, 43(3), 491–498.

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