Some structural properties of automata defined on groups

  • Roger W. Brockett
  • Alan S. Willsky
Submitted Abstract
Part of the Lecture Notes in Computer Science book series (LNCS, volume 25)


Finite Group Sequential System Coset Space Input String Isomorphism Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.W. Brockett and A.S. Willsky, "Finite Group Homomorphic Sequential Systems," IEEE Trans. on Automatic Control, Vol. AC-17, No. 4, August 1972, pp. 483–490.CrossRefMathSciNetGoogle Scholar
  2. 2.
    R.W. Brockett, "System Theory on Group Manifolds and Coset Spaces," SIAM Journal on Control, Vol. No. 2, 1972, pp. 265–284.Google Scholar
  3. 3.
    C.W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, N.Y., 1962.zbMATHGoogle Scholar
  4. 4.
    M. Hausner and J.T. Schwartz, Lie Groups; Lie Algebras, Gordon Breach, N.Y., 1970.Google Scholar
  5. 5.
    A. Isidori, "Direct Construction of Minimal Bilinear Realizations from Nonlinear Input/Output Maps," IEEE Trans. on Automatic Control, Vol. AC-18, No. 3, December 1973, pp. 626–631.CrossRefMathSciNetGoogle Scholar
  6. 6.
    M.A. Arbib and E.G. Manes, "Adjoint Machines, State-Behavior Machines, and Duality," COINS Technical Report 73B-1, Dept. of Computer and Information Science, University of Massachusetts at Amherst, Jan. 1973.Google Scholar
  7. 7.
    A.S. Willsky, Dynamical Systems Defined on Groups: Structural Properties and Estimation, Ph.D. Thesis, Dept. of Aeronautics and Astronautics, M.I.T., Cambridge, Mass., June 1973.Google Scholar
  8. 8.
    A.S. Willsky, "Invertibility Conditions for a Class of Finite State Systems Evolving on Groups," Proc. of the Eleventh Annual Allerton Conference, Univ. of Illinois, Oct. 3–5, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Roger W. Brockett
    • 1
  • Alan S. Willsky
    • 2
  1. 1.Division of Engineering and Applied PhysicsHarvard UniversityCambridgeUSA
  2. 2.Department of Electrical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations