Abstract
The state feedback pole assignment problem in control system design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. Fletcher, in these proceedings). A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature [13] [11], [1], but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system. Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references [2], [5], [6]), but these procedures are designed to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory.
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Kautsky, J., Nichols, N.K., van Dooren, P., Fletcher, L. (1983). Numerical Methods for Robust Eigenstructure Assignment in Control System Design. In: Deuflhard, P., Hairer, E. (eds) Numerical Treatment of Inverse Problems in Differential and Integral Equations. Progress in Scientific Computing, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-7324-7_13
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DOI: https://doi.org/10.1007/978-1-4684-7324-7_13
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