A Classification of Feedback Linearizable Mechanical Systems with 2 Degrees of Freedom

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


A classification of feedback linearizable mechanical control system with 2 DOF is proposed. We develop 3 types of linearization and for each we establish a normal form. Then, we characterize each class and calculate linearizing outputs. As a consequence, necessary and sufficient linearizability conditions are formulated for all cases. We illustrate our result by mechanical linearization of the TORA system.


Mechanical systems Feedback linearization Classification Normal forms 


  1. 1.
    Nijmeijer, H., van der Schaft, A.J.: Nonlinear Dynamical Control Systems. Springer-Verlag, New York (1990). ISBN 978-0-387-97234-3CrossRefGoogle Scholar
  2. 2.
    Respondek, W.: Introduction to geometric nonlinear control; linearization, observability and decoupling. In: Mathematical Control Theory No.1, Lecture Notes Series of the Abdus Salam, ICTP, vol. 8, Trieste (2001)Google Scholar
  3. 3.
    Jakubczyk, B., Respondek, W.: On linearization of control systems. Bull. Acad. Polonaise Sci. Ser. Sci. Math. 28, 517–522 (1980)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer-Verlag, Berlin (1995)CrossRefGoogle Scholar
  5. 5.
    Bullo, F., Lewis, A.D.: Geometric Control of Mechanical Systems. Modeling, Analysis and Design for Simple Mechanical Control Systems. Springer-Verlag, New York (2004)zbMATHGoogle Scholar
  6. 6.
    Respondek, W., Ricardo, S.: Equivariants of mechanical control systems. SIAM J. Control Optim. 51(4), 3027–3055 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Murray, M., Rathinam, M., Sluis, W.: Differential flatness of mechanical control systems: a catalog of prototype systems. In: ASME International Mechanical Engineering Congress and Exposition. Citeseer (1995)Google Scholar
  8. 8.
    Respondek, W., Ricardo, S.: On linearization of mechanical control systems. IFAC Proc. Volumes 45(19), 102–107 (2012)CrossRefGoogle Scholar
  9. 9.
    van der Schaft, A.: Linearization of Hamiltonian and gradient systems. IMA J. Math. Control Inf. 1, 185–198 (1984)CrossRefGoogle Scholar
  10. 10.
    Wan, C., Bernstein, D., Coppola, V.: Global stabilization of the oscillating eccentric rotor. Nonlinear Dyn. 10, 49–62 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesNormandie Université, INSA de RouenSaint-Etienne-du-RouvrayFrance
  2. 2.Institute of Automatic Control and RoboticsPoznan University of TechnologyPoznańPoland

Personalised recommendations