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Original Articles

The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

Pages 620-642 | Received 22 Jun 2007, Accepted 16 Mar 2008, Published online: 18 Mar 2009

References

  • Aranda-Bricaire , E , Kotta , U and Moog , C . 1996 . Linearization of Discrete-time Systems . SIAM Journal of Control Optimization , 34 : 1999 – 2023 .
  • Astrom , KJ and Wittenmark , B . 1984 . Computer Controlled Systems , Englewood Cliffs, NJ : Prentice Hall .
  • Conte , G , Moog , CH and Perdon , AM . 1999 . “ Nonlinear Control Systems ” . In An Algebraic Setting , London : Springer-Verlag .
  • Cox , D , Little , J and O'Shea , D . 1997 . “ Ideals, Varieties and Algorithms ” . In Graduate Text in Mathematics , New York : Springer-Verlag .
  • Cox , D , Little , J and O'Shea , D . 1998 . “ Using Algebraic Geometry ” . In Graduate Text in Mathematics , New York : Springer-Verlag .
  • Cruz-Hernandez , C , Alvarez-Gallegos , J and Castro-Linares , R . 1999 . Stability of Discrete Nonlinear Systems Under Nonvanishing Perturbations: Application to a Nonlinear Model-matching Problem . IMA Journal of Mathematical Control and Information , 16 : 23 – 41 .
  • Fliess , M and Glad , ST . 1994 . An Algebraic Approach to Linear and Non-linear Control , Sweden : Linköping University . Report Lith-ISY-R-1573
  • Fliess , M . 1992 . Reversible Linear and Nonlinear Discrete-time Dynamics . IEEE Transactions on Automatic Control , 37 : 1144 – 1153 .
  • Glad , ST . 1989 . “ Differential Algebraic Modeling of Nonlinear Systems ” . In Proceedings of MTNS-89 , 97 – 105 . Amsterdam .
  • Glad , T and Ljung , L . 2000 . Control Theory , London/New York : Taylor and Francis .
  • Glad , ST . 1990 . ‘Nonlinear Regulators and Ritt's Remainder Algorithm’ , Sweden : Linköping University . Report Lith-ISY-I-1097
  • Grizzle , JW . 1993 . A Linear Algebraic Framework for the analysis of Discrete-time Nonlinear Systems . SIAM Journal of Control Optimization , 31 : 1026 – 1044 .
  • Halas , M and Kotta , U . 2007 . “ Extension of the Concept of Transfer Function to Discrete-time Nonlinear Control Systems ” . In European Control Conference , Greece : Kos .
  • Isidori , A . 1985 . The Matching of a Prescribed Linear input–output Behaviour in a Nonlinear System . IEEE Trans. AC , 30 : 258 – 265 .
  • Kalouptsidis , N . 1997 . Signal Processing Systems, Theory and Design , New York : John Wiley and Sons .
  • Karafyllis , I and Kotsios , S . 2006 . Necessary and Sufficient Conditions for Robust Global Asymptotic Stabilization of Discrete Time Systems . Journal of Difference Equations and Applications , 12 : 741 – 768 .
  • Khalil , HK . 2002 . Nonlinear Systems , 3rd , New Jersey : Prentice Hall .
  • Kotsios , S . 2002 . On Detecting Solutions of Polynomials Nonlinear Difference Equations . Journal of Difference Equations and Applications , 8 : 551 – 571 .
  • Kotsios , S and Kalouptsidis: , N . 1993 . BIBO Stability Criteria for a Certain Class of Nonlinear Systems . International Journal of Control , 58 : 707 – 730 .
  • Kotsios , St and Kalouptsidis , N . 1993 . The Model Matching Problem for a Certain Class of Nonlinear Systems . International Journal of Control , 57 : 881 – 919 .
  • Kotsios , St . 2001 . An Application of Ritt's Remainder Algorithm to Discrete Polynomial Control Systems . IMA Journal of Mathematical Control and Information , 18 : 19 – 29 .
  • Kotsios , S . 2000 . A New Factorisation of Special Nonlinear Discrete Systems and Its Applications . IEEE, Transactions on Automatic Control , 45 : 24 – 33 .
  • Kotsios , S . 2005 . “ A Model Matching Algorithm for a Class of Nonlinear Discrete Systems ” . In A Symbolic Approach 44th IEEE Conference on Decision and Control and European Control Conference-05 Seville, , Spain
  • Kotsios , S . 2007 . “ The Linear Factors of Nonlinear Discrete Systems With Cross-products and Their Application to the Model Matching Problem ” . In European Control Conference-07 Kos, , Greece
  • Kotsios , St and Lappas , D . 1996 . A Description of 2-Dimensional Discrete Polynomial Dynamics . IMA Journal of Mathematical Control and Information , 13 : 409 – 428 .
  • Kotta , U . 1995 . “ Inversion Method in the Discrete-time Nonlinear Control Systems Syntesis Problems ” . In Lecture Notes in Control and Information Sciences , Vol. 205 , New York : Springer-Verlag .
  • Kotta , U . 2000 . “ Irreducibility Conditions for Nonlinear input–output Difference Equations ” . In 39th IEEE Conf. on Decision and Control Sydney, , Australia
  • Kotta , U , Zinober , ASI and Liu , P . 2001 . Transfer Equivalence and Realization of Nonlinear Higher Order input–output Difference Equations . Automatica , 37 : 1771 – 1778 .
  • Monaco , S and Normand-Cyrot , D . 1997 . “ On Nonlinear Digital Control ” . In Nonlinear Systems , 127 – 155 . London : Chapman & Hall .
  • Monaco , S and Normand-Cyrot , D . 2007 . Advanced Tools for Nonlinear Sampled-data Systems' Analysis and Control . European Journal of Control , 13 : 221 – 241 .
  • Munro , N . 1999 . Symbolic Methods in Control Systems and Design . IEE Control Engineering Series , 56
  • Nijmeijer , H and van der Schaft , A . 1990 . Nonlinear dynamical control systems , New York : Springer-Verlag .
  • Rugh , JW . 1981 . Nonlinear System Theory , Baltimore : The John Hopkins University Press .
  • Sontag , DE . 1979 . “ Polynomial Response Maps ” . In Lecture Notes in Control and Information Sciences , New York : Springer-Verlag .
  • Sontag , ED . 1977 . Realization theory of Discrete-time Nonlinear Systems: Part I–the Bounded Case . IEEE Transactions of Circuits and Systems , 10 : 342 – 356 .
  • Sontag , DE . 1990 . “ Mathematical Control theory ” . In Texts in Applied Mathematics , Vol. 6 , New York Inc : Springer-Verlag .
  • Stetter , HJ . 2004 . Numerical Polynomial Algebra , Philadelphia, PA : SIAM .
  • Sturmfels , B . 2002 . “ Solving Polynomial Equations ” . In unpublished notes, for lectures given at the CBMS Conference at Texas A and M University College Station
  • Wu , W-T . On algebricodifferential equation solving . www.mmrc.iss.ac.cn/pub/mm22.pdf/2.pdf (accessed Dec 2003)
  • Yamanaka , O , Ohmori , H and Sano , A . 1997 . Design Method of Exact Model-Matching Control for Finite Volterra Series Systems . International Journal of Control , 68 : 107 – 124 .
  • Yeh , P-C and Kokotovic , PV . 1995 . Adaptive Output-feedback Design for a Class of Nonlinear Discrete-time Systems . IEEE Trans. on Aut. Control , 40 : 1663 – 1668 .
  • Zhang , C and Zheng , Y . 2004 . A Polynomial Approach to Discrete-time Nonlinear System Controllability . International Journal of Control , 77 : 491 – 497 .

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