Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2008.14.3.226

Direction Assignment of Left Eigenvector in Linear MIMO System  

Kim, Sung-Hyun (연세대학교 기계공학부)
Yang, Hyun-Seok (연세대학교 기계공학부)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.14, no.3, 2008 , pp. 226-231 More about this Journal
Abstract
In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.
Keywords
eigenstructure assignment; left eigenvector direction; state feedback;
Citations & Related Records

Times Cited By SCOPUS : 1
연도 인용수 순위
  • Reference
1 B. C. Moore, "On the flexibility offered by state feedback in multivariable systems beyond closed loop eigenvalue assignment," IEEE Trans. Automat. Contr., 21, 689-692, 1976   DOI
2 J. W. Choi, "A simultaneous assignment methodology of right/left eigenstructures," IEEE Trans. On Aerospace and Electronic systems, 34, 2, 625-634, 1998   DOI   ScienceOn
3 G. Duan, "Eigenstructure assignment in descriptor systems via output feedback: a new complete parametric approach," Int. J. Contr., 72, 4, 345-364, 1999   DOI   ScienceOn
4 S. P. Burrows and R. J. Patton, "Design of a low-sensitivity, minimum norm and structurally constrained control law using eigenstructure assignment," Optimal Contr. App. Methods, 12, 131-140, 1991   DOI
5 J. E. Ensor, "Analysis on eigenmode sensitivity to structured uncertainty," Prec. of the American Contr. Conf., 2002
6 Q, Zhang, G. L. Slater, and R. J. Allemang, "Suppression of undesired inputs of linear systems by eigenspace assignment," J. Guidance Control and Dynamics, 13, 3, 1990
7 J. W. Choi, J. G. Lee, and Y. Kim, "Design of an effective controller via disturbance accommodating left eigenstructure assignment," J. of Guidance Control and Dynamics, 18, 2, 347- 354, 1995   DOI   ScienceOn
8 K. M. Sobel, E. Y. Shapiro, and A. N. Andry, "Eigenstructure assignment," Int. J. Contr., 59, 1, 13-37, 1994   DOI   ScienceOn
9 J. Kautsky, N. K. Nichols, and P. Van Dooren, "Robust pole assignment in linear state feedback," Int. J. Contr., 41, 5, 1129- 1155, 1985   DOI   ScienceOn
10 W. M. Wonham, "On pole assignment in multi-input controllable linear systems," IEEE Trans. on Automat. Contr., 12, 6, 1967
11 G. P. Liu and R. J. Patton, Eigenstructure Assignment for Control System Design, John Wiley & Sons, 1998
12 G. Duan, "On the solution to the Sylvester matrix equation AV+BW=EVF," IEEE. Trans. on Automat. Contr., 41, 4, 612- 614, 1996   DOI   ScienceOn