Orthogonality and partial pole assignment for the symmetric definite quadratic pencil. (English) Zbl 0876.15009

A second order matrix DE is reinterpreted as an eigenvalue and eigenvector problem for a quadratic matrix pencil. This paper establishes orthogonality relations for the resulting symmetric definite pencils and gives explicit and realizable feedback rules for partial pole assignment of the underlying system.
Reviewer: F.Uhlig (Auburn)


15A22 Matrix pencils
93B55 Pole and zero placement problems
15A18 Eigenvalues, singular values, and eigenvectors
93B52 Feedback control
Full Text: DOI


[1] Balas, M. J., Trends in large space structure control theory: Fondest dreams, wildest hopes, IEEE Trans. Automat. Control, AC-22, 522-535 (1982) · Zbl 0496.93007
[2] Bhaya, A.; Desoer, C., On the design of large flexible space structures (lfss), IEEE Trans. Automat. Control, AC30, 11, 1118-1120 (1985) · Zbl 0574.93044
[3] Boley, D.; Golub, G. H., A survey of matrix inverse eigenvalue problems, Inverse Problems, 3, 595-622 (1987) · Zbl 0633.65036
[4] Caughey, T. K.; O’Kelly, M. E.J., Classical normal modes in damped linear dynamic systems, J. Appl. Mech., 32, 583-588 (1965)
[5] Datta, B. N., Linear and numerical linear algebra in control theory: Some research problems, Linear Algebra Appl., 197,198, 755-790 (1994) · Zbl 0798.15015
[6] Datta, B. N., Numerical Linear Algebra and Applications (1995), Brooks/Cole: Brooks/Cole Pacific Grove, Calif
[7] Datta, B. N.; Saad, Y., Arnoldi methods for large Sylvester-like observer matrix equations and an associated algorithm for partial pole assignment, Linear Algebra Appl., 154-156, 225-244 (1991) · Zbl 0734.65037
[8] Inman, D., Vibration with Control, Measurement and Stability (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J
[9] Laub, A. J.; Arnold, W. F., Controllability and observability criteria for multivariate linear second order models, IEEE Trans. Automat. Control, AC-29, 163-165 (1984) · Zbl 0543.93005
[10] Parlett, B. N.; Chen, H. C., Use of indefinite pencils for computing damped natural modes, Linear Algebra Appl., 140, 53-88 (1990) · Zbl 0725.65055
[11] Saad, Y., Projection and deflation methods for partial pole assignment in linear state feedback, IEEE Trans. Automat. Control, 33, 290-297 (1988) · Zbl 0641.93031
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