Stability of quaternionic linear systems

IEEE Transactions on Automatic Control

Volumn 51, Issue 3, 2006, Pages 518-523

  Pereira, Ricardo ^a   Vettori, Paolo ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Behaviors; Quarternions; Stability

Indexed keywords

MATRIX ALGEBRA; POLYNOMIALS; SYSTEM STABILITY;

ALGEBRAIC PROPERTIES; BOUNDED-INPUT-BOUNDED-OUTPUT (BIBO); QUATERNIONIC DYNAMICAL SYSTEMS; QUATERNIONIC LINEAR SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 33644942141     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.864202     Document Type: Article

References (18)

1. P. B. Visscher and X. Feng, "Quaternion-based algorithm for micromagnetics," Phys. Rev. B, vol. 65, no. 104 412, 2002.
2. D. Hestenes, New Foundations for Classical Mechanics. Dordrecht, The Netherlands: Kluwer, 1986.
3. J. B. Kuipers, Quaternions and Rotation Sequences. Princeton, NJ: Princeton Univ. Press, 1999.
4. A. El-Gohary and E. R. Elazab, "Exponential control of a rotational motion of a rigid body using quaternions," Appl. Math. Comput., vol. 137, no. 2-3, pp. 195-207, 2003.
5. M. Hazewinkel and C. Martin, "On decentralization, symmetry and special structure in linear systems," Erasmus Universiteit Rotterdam, Econometrisch Institunt, Tech. Rep. R8201/M, 1982.
6. A. Rodriguez and M. Athans, "Multivariable control of a twin-lift helicopter system using the LQG/LTR design methodology," in Proc. Amer. Control Conf., Seattle, WA, Jun. 1986, pp. 1325-1332.
7. S. D. Leo, G. C. Ducati, and C. C. Nishi, "Quaternionic potentials in nonrelativistic quantum mechanics," J. Phys. A, vol. 35, no. 26, pp. 5411-5426, 2002.
8. S. D. Leo and G. C. Ducati, "Real linear quaternionic differential operators," Comput. Math. Appl., vol. 48, no. 12, pp. 1893-1903, 2004.
9. J. C. Willems, "Models for dynamics," in Dynamics Reported. Chichester, U.K.: Wiley, 1989, vol. 2, pp. 171-269.
10. F. Zhang, "Quaternions and matrices of quaternions," Linear Alg. Appl., vol. 251, pp. 21-57, 1997.
11. R. Pereira, P. Rocha, and P. Vettori, "Algebraic tools for the study of quaternionic behavioral systems," Linear Alg. Appl., vol. 400, pp. 121-140, 2005.
12. T. Y. Lam, A First Course in Noncommutative Rings. New York: Springer-Verlag, 1991.
13. O. Ore, "Linear equations in noncommutative fields," Ann. Math. (2), vol. 32, no. 3, pp. 463-477, 1931.
14. N. Jacobson, The Theory of Rings. Providence, RI: AMS, 1943.
15. J. C. Willems, "Paradigms and puzzles in the theory of dynamical systems," IEEE Trans. Autom. Control, vol. 36, no. 3, pp. 259-294, Mar. 1991.
16. J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory: A Behavioral Approach, ser. Texts in Applied Mathematics. Berlin, Germany: Springer-Verlag, 1997, vol. 26.
17. R. M. Guralnick, L. S. Levy, and C. Odenthal, "Elementary divisor theorem for noncommutative PIDs," in Proc. Amer. Math. Soc., vol. 103, 1988, pp. 1003-1011.
18. M. Vidyasagar, Control System Synthesis. Cambridge, MA: MIT Press, 1985.