Abstract
In Chu (Syst Control Lett 56:303–314, 2007), the pole assignment problem was considered for the control system \(\dot{x} = Ax + Bu\) with linear state-feedback \(u = Fx.\) An algorithm using the Schur form has been proposed, producing good suboptimal solutions which can be refined further using optimization. In this paper, the algorithm is improved, incorporating the minimization of the feedback gain \(\|F\|.\) It is also extended for the pole assignment of the descriptor system \(E\dot{x} = Ax + Bu\) with linear state- and derivative-feedback \(u = Fx - G\dot{x}.\) Newton refinement for the solutions is discussed and several illustrative numerical examples are presented.
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References
Beattie C, Ipesn ICF (2003) Inclusion regions for matrix eigenvalues. Lin Alg Appl 358:281–291
Braconnier T, Saad Y (1998) Eigenvalue bounds from the Schur form. Research report. University of Minnesota Supercomputing Institute UMSI 98/21
Cho GE, Ipsen ICF (1997) If a matrix has only a single eigenvalue, how sensitive is this eigenvalue? CRSC Technical report, North Carolina State University, Raleigh NC, TR97-20
Cho GE, Ipsen ICF (1998) If a matrix has only a single eigenvalue, how sensitive is this eigenvalue? II, CRSC technical report, North Carolina State University, Raleigh NC, TR98-8
Chu K-WE (1988) A controllability condensed form and a state feedback pole assignment algorithm for descriptor systems. IEEE Trans Autom Control 33:366–370
Chu EK-W (2001) Optimization and pole assignment in control system. Int J Appl Maths Comp Sci 11:1035–1053
Chu EK-W (2007) Pole assignment via the Schur form. Syst Control Lett 56:303–314
Duan G-R, Patton RJ (1999) Robust pole assignment in descriptor systems via proportional plus partial derivative state feedback. Int J Control 72:1193–1203
Golub GH, Van Loan CF (1989) Matrix Computations. 2nd edn. Johns Hopkins University Press, Baltimore, MD
Grippo L, Sciandrone M (2002) Nonmonotone globalization techniques for the Barzilai-Borwein gradient method. Comput Optim Applics 23:143–169
Henrici P (1962) Bounds for iterates, inverses, spectral variation and the field of values of nonnormal matrcies. Numer Math 4:24–40
Kautsky J, Nichols NK, Chu K-WE (1989) Robust pole assignment in singular control systems. Lin Alg Applic 121:9–37
Kautsky J, Nichols NK, Van Dooren P (1985) Robust pole assignment via in linear state feedback. Int J Control 41:1129–1155
Mathworks (2002) MATLAB User’s Guide
Stewart GW, Sun J-G (1990) Matrix Perturbation Theory. Academic Press, New York
Sun J-G (2001) Perturbation Theory of Matrices (in Chinese), 2nd ed., Science Press
White BA (1995) Eigenstructure assignment: a survey. Proc Instn Mech Engrs 209:1–11
Varga A (2003) A numerical reliable approach to robust pole assignment for descriptor systems. Future Generation Comp Syst 19:1221–1230
Acknowledgements
We would like to thank Professor Shu-Fang Xu (Beijing University, China) for various interesting discussions and much encouragement.
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Li, T., Chu, E.Kw., Lin, WW. (2011). Robust Pole Assignment for Ordinary and Descriptor Systems via the Schur Form. In: Van Dooren, P., Bhattacharyya, S., Chan, R., Olshevsky, V., Routray, A. (eds) Numerical Linear Algebra in Signals, Systems and Control. Lecture Notes in Electrical Engineering, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0602-6_16
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DOI: https://doi.org/10.1007/978-94-007-0602-6_16
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