Robust Predictive Control of Singular Systems with Structured Feedback Uncertainty

  • Xiaohua Liu
  • Rong Gao
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 269)


The problem of output feedback robust model predictive control is presented for the singular systems with structured feedback uncertainties which is described into linear fractional model. When the system states are immeasurable, the sufficient conditions for the existence of output feedback controller are obtained by linear matrix inequalities. The infinite time domain “min-max” optimization problem is converted into convex optimization problem. The robust stability of the closed-loop singular systems is guaranteed by the initial feasible solution of the optimization problem.The regularity and the impulse-free of singular systems are also held. A simulation example shows the effectiveness of the method.


Robust predictive control Singular systems Uncertainty Output feedback Linear matrix inequalities 



This work is supported by National Nature Science Foundation under Grant 61174097.


  1. 1.
    Marija D, Marko S (2009) Singular systems, state feedback problem. Linear Algebra Appl 4(24):1267–1292Google Scholar
  2. 2.
    Kothare MV, Balakrishnan V, Morari M (1996) Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10):1361–1379CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Kouvaritakis B, Rossiter JA, Schuurmans J (2000) Efficient robust predictive control. IEEE Trans Autom Control 45(8):1545–154Google Scholar
  4. 4.
    Lee YI, Kouvaritakis B (2006) Constrained robust model predictive control based on periodic invariance. Automatica 42(12):2175–2181CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Francesco A, Cuzzola J, Geromel C, Manfred M (2002) An improved approach for constrained robust model predictive control. Automatica 38(7):1183–1189CrossRefMATHGoogle Scholar
  6. 6.
    Zhang L, Huang B (2004) Robust model predictive control of singular systems. IEEE Trans Autom Control 49(6):1000–1006CrossRefGoogle Scholar
  7. 7.
    Liu XH, Wang LJ (2009) Robust model predictive control for singular systems via dynamic output feedback. Control Decision 24(9):1371–1376Google Scholar
  8. 8.
    Lee SM, Park JH (2007) Output feedback model predictive control for LPV systems using parameter dependent Lyapunov function. Appl Math Comput 190(1):671–676CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Xiaohua Liu
    • 1
  • Rong Gao
    • 1
  1. 1.School of Mathematics and InformationLudong UniversityYantaiPeople’s Republic of China

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