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Multistage parametric eigenstructure assignment by output-feedback control. (English) Zbl 0688.93023

An efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output-feedback control is developed. The sets of closed-loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages.
This allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions. The number of effective free parameters beyond eigenvalue assignment is determined, and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced.
Furthermore, a simple criterion for individual eigenvalue assignability is established, and the irregular behaviour of a special class of systems is explained in terms of an interesting property that the protection of a specific eigenvalue may be unavoidably extended to some other eigenvalue.
The paper is well organized and written and can be considered to be of a very good quality in its topic area.
Reviewer: A.V.Machias

MSC:

93B55 Pole and zero placement problems
15A18 Eigenvalues, singular values, and eigenvectors
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
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References:

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