Infinite eigenvalue assignment in descriptor systems via state feedback

Abstract

The problem of infinite eigenvalue assignment in the descriptor system via state feedback control u = Kx is considered. The problem is related to a group of recursive equations. By proposing a general complete parametric solution to this group of recursive equations, a general complete parametric approach is presented for the proposed infinite eigenvalue assignment problem. General parametric forms of the closed-loop eigenvectors and the feedback gain matrix are given in terms of certain parameter vectors which represent the design degrees of freedom. The approach involves mainly a singular value decomposition of the matrix E and a singular value decomposition of a lower dimension matrix, and thus is very simple and requires less computational work. Moreover, it overcomes the defects of some previous works. An example is given to illustrate the effect of the approach.

Keywords:

• infinite eigenvalue assignment
• state feedback
• closed-loop regularity
• descriptor systems
• pole placement

Acknowledgements

Biao Zhang is grateful to the anonymous reviewers for their helpful comments and suggestions. This work was supported by the Chinese National Natural Science Foundation under Grant No. 10671046.