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Original Articles

Stabilising compensators for linear time-varying differential systems

Pages 701-721 | Received 24 Apr 2015, Accepted 04 Sep 2015, Published online: 13 Oct 2015

References

  • Anderson, B.D.O., Ilchmann, A., & Wirth, F.R. (2013). Stabilizability of linear time-varying systems. Systems and Control Letters, 62, 747–755.
  • Berger, T., Ilchmann, A., & Wirth, F.R. (2014). Zero dynamics and stabilization for analytic linear systems. Acta Applicandae Mathematicae, 138, 17–57.
  • Blumthaler, I. (2012). Stabilisation and control design by partial output feedback and by partial interconnection. International Journal of Control, 85, 1717–1736.
  • Blumthaler, I., & Oberst, U. (2012). Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules. Linear Algebra and its Applications, 436, 963–1000.
  • Bourlès, H., & Marinescu, B. (2011). Linear time-varying systems. Berlin: Springer.
  • Bourlès, H., Marinescu, B., & Oberst, U. (2015a). Exponentially stable linear time-varying discrete behaviors. SIAM Journal on Control and Optimization, 53, 2725–2761.
  • Bourlès, H., Marinescu, B., & Oberst, U. (2015b). Weak exponential stability of linear time-varying differential behaviors. Linear Algebra and its Applications, 486, 523–571.
  • Callier, F.M., & Desoer, C.A. (1982). Multivariable feedback systems. New York, NY: Springer.
  • Chen, C.-T. (1984). Linear system theory and design. FortWorth, TX: Harcourt Brace.
  • Chyzak, F., Quadrat, A., & Robertz, D. (2007). OreModules: A symbolic package for the study of multidimensional linear systems. In J. Chiasson, & J.-J. Loiseau (Eds.), Applications of time-delay systems (pp. 233–264). Berlin: Springer.
  • Cohn, P.M. (2006). Free ideal rings and localization in general rings. Cambridge: Cambridge University Press.
  • Fliess, M. (1990). Some basic structural properties of generalized linear systems. Systems and Control Letters, 15, 391–396.
  • McConnell, J.C., & Robson, J.C. (1987). Noncommutative noetherian rings. Chichester: John Wiley and Sons.
  • Phat, V.N., & Jeyakumar, V. (2010). Stability, stabilization and duality for linear time-varying systems. Optimization, 59, 447–460.
  • Quadrat, A. (2006). On a generalization of the Youla-Kučera parametrization. Part II: The lattice approach to MIMO system. Mathematics of Control, Signals and Systems, 18, 199–235.
  • Quadrat, A. (2010). Systèmes et Structures: Une approche de la théorie des systèmes par l’analyse algébrique constructive ( Thèse d‘habilitation à diriger des recherches) [Systems and Structures: An approach to systems theory by constructive algebraic analysis (Habilitation thesis for supervising research)]. Université de Nice Sofia-Antipolis.
  • Quadrat, A. (2015). Algebraic analysis of linear functional systems. Book in preparation.
  • Ravi, R., Pascoal, A.M., & Khargonekar, P.P. (1992). Normalized coprime factorizations for linear time-varying systems. Systems and Control Letters, 18, 455–465.
  • Robertz, D. (2015). Recent progress in an algebraic analysis approach to linear systems. Multidimensional Systems and Signal Processing, 26, 349–388. doi:10.1007/s11045-014-0280-9
  • Rugh, W.J. (1996). Linear system theory. Upper Saddle River, NJ: Prentice Hall.
  • van der Put, M., & Singer, M.F. (2003). Galois theory of linear differential equations. Berlin: Springer.
  • Vidyasagar, M. (1985). Control system synthesis: A factorization approach. Cambridge, MA: The MIT Press.

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