Algebraic tools for the study of quaternionic behavioral systems

Linear Algebra and Its Applications

Volumn 400, Issue 1-3, 2005, Pages 121-140

  Pereira, Ricardo ^a   Rocha, Paula ^a   Vettori, Paolo ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Behavioral approach; Linear systems; Quaternions; Smith form

Indexed keywords

ASYMPTOTIC STABILITY; CONTROLLABILITY; DIFFERENCE EQUATIONS; LINEAR SYSTEMS; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING;

BEHAVORIAL APPROACH; NONCOMMUTATIVE ALGEBRA; QUATERNIONS; SMITH FORM;

LINEAR ALGEBRA;

EID: 15844411904     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.01.008     Document Type: Article

References (17)

1. S.P. Brumby, and G.C. Joshi Experimental status of quaternionic quantum mechanics Chaos Solitons Fractals 7 5 1996 747 752
2. S. De Leo, and G. Ducati Quaternionic differential operators J. Math. Phys. 42 5 2001 2236 2265
3. A. El-Gohary, and E.R. Elazab Exponential control of a rotational motion of a rigid body using quaternions Appl. Math. Comput. 137 2-3 2003 195 207
4. M. Hazewinkel, J. Lewis, and C. Martin Symmetric systems with semisimple structure algebra: the quaternionic case Syst. Control Lett. 3 3 1983 151 154
5. D. Hestenes New Foundations for Classical Mechanics 1986 Kluwer Academic Publishers Group Dordrecht, The Netherlands
6. N. Jacobson The Theory of Rings 1943 American Mathematical Society New York
7. B. Jancewicz Multivectors and Clifford Algebra in Electrodynamics 1988 World Scientific Publishing Co. Inc. Teaneck, NJ
8. J.B. Kuipers Quaternions and Rotation Sequences 1999 Princeton University Press Princeton, NJ
9. T.Y. Lam A First Course in Noncommutative Rings 1991 Springer-Verlag New York
10. J.W. Polderman, and J.C. Willems Introduction to Mathematical Systems Theory: A Behavioral Approach Texts in Applied Mathematics vol. 26 1997 Springer-Verlag Berlin
11. M. Vidyasagar Control System Synthesis 1985 MIT Press Cambridge, MA
12. P.B. Visscher, and X. Feng Quaternion-based algorithm for micromagnetics Phys. Rev. B 65 104412 2002
13. J. Vrbik A novel solution to Kepler's problem Eur. J. Phys. 24 6 2003 575 583
14. J.C. Willems From time series to linear system-part I. Finite dimensional linear time invariant systems Automatica-J. IFAC 22 5 1986 561 580
15. J.C. Willems Models for dynamics U. Kirchgraber H.O. Walther Dynamics Reported vol. 2 1989 John Wiley & Sons Ltd. Chichester 171 269
16. J.C. Willems Paradigms and puzzles in the theory of dynamical systems IEEE Trans. Automat. Control 36 3 1991 259 294
17. F. Zhang Quaternions and matrices of quaternions Linear Algebra Appl. 251 1997 21 57