A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm

  • Maria Domenia Di Benedetto
Part of the Mathematics and Its Applications book series (MAIA, volume 29)


Consider a nonlinear system of the form
$$ \dot{x} = f(x) + \sum\limits_{{i = 1}}^m {{g_i}(x){u_i}} y = h(x) $$
with state x ∈ X Ì ℝn, input u ∈ ℝm and output y ∈ ℝP; f and g1,...,gm are analytic vector fields on X and h is an analytic function.


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  1. [1]
    A.J. Krener: (Adf,g),(adf,g) and Locally (adf,g) Invariant and Controllability Distributions. SIAM J. Control and Optimization, 23, 523–549, (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    A. Isidori, A.J. Krener, C. Gori-Giorgi, S. Monaco: Nonlinear Decoupling via Feedback: A Differential-Geometric Approach IEEE Trans. Automat. Contr., Vol. AC-26, 331–345, (1981).MathSciNetCrossRefGoogle Scholar
  3. [3]
    H. Nijmeijer, J.M. Schumacher: Zeros at Infinity for Affine Nonlinear Control Systems. IEEE Trans. Automat. Contr., Vol. AC-30, 566–573, (1985).MathSciNetCrossRefGoogle Scholar
  4. [4]
    M.D. Di Benedetto, A. Isidori: The Matching of Nonlinear Models via Dynamic State Feedback. Proc. 23rd CDC, Las Vegas, (Dec. 1984), to appear on SIAM J. of Contr. and Optimization.Google Scholar
  5. [5]
    H. Nijmeijer: Right-invertibility for nonlinear control systems: a geometric approach. Memo. 484, Dept. Appl. Math., Twente University of Technology, (1984).Google Scholar
  6. [6]
    A. Isidori, A. Ruberti: On the Synthesis of Linear Input-Output Responses for Nonlinear Systems. Sys. Control Lett. 4, 17–22, (1984).MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    A. Isidori: Nonlinear Control Systems: an Introduction. Lect. Notes in Control and Information Science, Vol. 72, Springer-Verlag, (1985).zbMATHCrossRefGoogle Scholar
  8. [8]
    A. Isidori: Control of Nonlinear Systems via Dynamic State Feedback. Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel eds., Reidel, Dordrecht, (1986). This volume.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Maria Domenia Di Benedetto
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomeItaly

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