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1996•Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control EngineeringRequires access

On Eigenvectors and Generalized Eigenvectors in Multi-Variable Descriptor Control Systems

Shuai Liu, Ron J. Patton

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Abstract

This paper is concerned with an eigenvector problem in multi-variable descriptor control systems. It proves that the eigenvectors and generalized eigenvectors premultiplied by the singular matrix E of the descriptor system as well as the eigenvectors and the generalized eigenvectors, which play a very important role in the design of multi-variable descriptor systems via eigenstructure assignment, are linearly independent.

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What this paper is about

This paper is concerned with an eigenvector problem in multi-variable descriptor control systems. It proves that the eigenvectors and generalized eigenvectors premultiplied by the singular matrix E of the descriptor system as well as the eigenvectors and the generalized eigenvectors, which play a very important role in the design of multi-variable descriptor systems via eigenstructure assignment, are linearly independent.

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Available abstract

This paper is concerned with an eigenvector problem in multi-variable descriptor control systems. It proves that the eigenvectors and generalized eigenvectors premultiplied by the singular matrix E of the descriptor system as well as the eigenvectors and the generalized eigenvectors, which play a very important role in the design of multi-variable descriptor systems via eigenstructure assignment, are linearly independent.

Key concepts: Eigenvalues and eigenvectors, Defective matrix, Eigenvalues and eigenvectors of the second derivative, Modal matrix, Variable (mathematics), Eigenvalue perturbation, Generalized eigenvector, Mathematics

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