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Explicit Determination of State Feedback Matrices
Electrical Engineering Department, The University of Jordan, Amman, Jordan
- 1 Electrical Engineering Department, The University of Jordan, Amman, Jordan
Advances in Pure Mathematics·Volume 05 (2015)·Pages 403–412·Published 29 May 2015·DOI10.4236/apm.2015.57040
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Abstract
Methods which calculate state feedback matrices explicitly for uncontrollable systems are considered in this paper. They are based on the well-known method of the entire eigenstructure assignment. The use of a particular similarity transformation exposes certain intrinsic properties of the closed loop w-eigenvectors together with their companion z-vectors. The methods are extended further to deal with multi-input control systems. Existence of eigenvectors solution is established. A differentiation property of the z-vectors is proved for the repeated eigenvalues assignment case. Two examples are worked out in detail.
KeywordsState FeedbackEigenstructure AssignmentPole PlacementExplicit Methods
- El-Ghezawi, O.M.E. (2003) Explicit Formulae for Eigenstructure Assignment. Proceedings of the 5th Jordanian International Electrical and Electronic Engineering Conference, Amman, 13-16 October 2003, 183-187.
- Porter, B. and D’Azzo, J.J. (1977) Algorithm for the Synthesis of State-Feedback Regulators by Entire Eigenstructure Assignment. Electronic Letters, 13, 230-231. http://dx.doi.org/10.1049/el:19770167
- D’azzo, J.J. and Houpis, C.H. (1995) Linear Control Systems: Analysis and Design. 4th Edition, McGraw-Hill, New York.
- Sobel, K.M., Shapiro, E.Y. and Andry, A.N. (1994) Eigenstructure Assignment. International Journal of Control, 59, 13-37. http://dx.doi.org/10.1080/00207179408923068
- White, B.A. (1995) Eigenstructure Assignment: A Survey. Proceedings of the Institution of Mechanical Engineers, 209, 1-11. http://dx.doi.org/10.1080/00207179408923068
- Liu, G.P. and Patton, R.J. (1998) Eigenstructure Assignment for Control System Design. John Wiley & Sons, New York.
- Mimins, G. and Paige, C.C. (1982) An Algorithm for Pole Assignment of Time Invariant Linear Systems. International Journal of Control, 35, 341-354. http://dx.doi.org/10.1080/00207178208922623
- Ramadan, M.A. and El-Sayed, E.A. (2006) Partial Eigenvalue Assignment Problem of Linear Control Systems Using Orthogonality Relations. Acta Montanistica Slovaca Roník, 11, 16-25.
- Datta, B.N. and Sarkissian, D.R. (2002) Partial Eigenvalue Assignment in Linear Systems: Existence, Uniqueness and Numerical Solution. http://www3.nd.edu/~mtns/papers/70_3.pdf http://www.math.niu.edu/~dattab/psfiles/paper.mtns.2002.pdf
- Lancaster, P. and Tismentasky, M. (1985) The Theory of Matrices with Applications. 2nd Edition, Academic Press, Waltham, Massachusetts.
- Graybill, F.A. (1983) Matrices with Applications in Statistics. Wadsworth Publishing Company, Belmont.
- Green, P.E. and Carroll, J.D. (1976) Mathematical Tools for Applied Multivariate Analysis. Academic Press, Waltham, Massachusetts.
- Schott, J.R. (1997) Matrix Analysis for Statistics. John Wiley, New York.