Abstract
This paper examines the problem of arbitrary pole assignment by decentralized output feedback. New sufficient conditions for the existence of real solutions are derived in terms of the heights of the first Whitney classes corresponding to the channel pairs ofm i outputs, pi inputs, and some appropriate partitioning of the number of states. These results extend the odd intersection framework approach based on the heights to the decentralized case and provide sufficient conditions for cases not covered by previous results.
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References
B. D. O. Anderson and D. J. Clements (1981), Algebraic characterization of fixed modes in decentralized control,Automatica,17, 703–712.
R. W. Brockett and C. I. Byrnes (1981), Multivariable Nyquist criteria, root loci and pole placement,IEEE Trans. Automat. Control,26, 271–285.
C. I. Byrnes (1983), Stabilizability of multivariable systems and the Ljusternik-Snirelmann category of real Grassmannians,Systems Control Lett.,3, 255–262.
E. J. Davison and S. H. Wang (1975),IEEE Trans. Automat. Control,20, 516–518.
A. Dold (1980),Lectures on Algebraic Topology, Springer-Verlag, New York.
C. Giannacopoulos and N. Karcanias (1985), Pole assignment of strictly proper systems by constant output feedback.Internat. J. Control,42, 543–565.
P. Griffiths and J. Harris (1978),Principles of Algebraic Geometry, Wiley, New York.
R. Hermann and C. Martin (1975), Applications of algebraic geometry to systems theory—part l,IEEE Trans. Automat. Control,22, 19–25.
W. V. D. Hodge and D. Pedoe (1952),Methods of Algebraic Geometry, Vol. 2, Cambridge University Press, London.
N. Karcanias and C. Giannacopoulos (1984), On Grassmann invariants, almost zeros and the determinantal zero, pole assignment of linear systems,Internat. J. Control,40, 673–698.
N. Karcanias and C. Giannacopoulos (1989), Necessary and sufficient conditions for zero assignment by constant squaring down,Linear Algebra Appl., 415–446.
N. Karcanias, B. Laios, and C. Giannacopoulos (1988), Decentralized determinantal assignment problems: fixed and almost fixed modes and zeros,Internat. J. Control,23, 149–181.
S. Kleiman and D. Laksov (1972), Schubert calculus,Amer. Math. Monthly,79.
B. A. Laios (1990), A Unified Approach to Decentralized Control, Ph.D. thesis, Control Engineering Centre, City University, London.
J. Leventides (1993), Algebrogeometric and Topological Methods in Control Theory, Ph.D. thesis, City University, London.
J. Leventides and N. Karcanias (1992), A new sufficient condition for arbitrary pole placement by real constant output feedback,Systems Control Lett.,3, 191–200.
J. Leventides and N. Karcanias (1995), Global symptotic linearization of the pole placement map: a closed form solution for the output feedback problem,Automatica,31, 1303–1309.
M. Marcus and H. Mine (1969),A Survey of Matrix Theory and Matrix Inequalities, Dover, New York.
D. Mumford (1976),Algebraic Geometry, I: Complex Projective Varieties, Springer-Verlag, New York.
J. Rosenthal (1992), New results in pole assignment by real output feedback,SIAM J. Control Optim.,30, 203–211.
J. Rosenthal, J. M. Schumacher, and J. C. Willems (1994), Generic Eigenvalue Assignment by Memoryless Real Output Feedback, Report, CWI, Amsterdam.
R. E. Stong (1982), Cup products in Grassmannians,Topology Appl.,13, 103–113.
X. Wang (1994), Decentralized pole assignment and product Grassmannians,SIAM J. Control Optim.,32, 855–875.
X. Wang (1994) Grassmannian, Central Projection and Output Feedback Pole Assignment of Linear Systems, Preprint.
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This research has been supported by EPSRC Grant GR/H 20466, U.K.
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Leventides, J., Karcanias, N. Sufficient conditions for arbitrary pole assignment by constant decentralized output feedback. Math. Control Signal Systems 8, 222–240 (1995). https://doi.org/10.1007/BF01211860
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DOI: https://doi.org/10.1007/BF01211860