Sequential eigenstructure assignment with minimal state‐feedback gain†

Abstract

This paper proposes a practical and sequential eigenstructure assignment method for designing a parametric state‐feedback controller in multi‐input linear time‐invariant systems. This approach, which sequentially shifts a prescribed set of self ‐conjugate multiple eigenvalues to the closed‐loop system, can explicitly parameterize in groups, and is very useful. Spectrum‐invariant free parameters are proposed to simultaneously deal with two problems: (i) assigning the desired corresponding eigenvectors and generalized eigenvectors within an admissible class, and (ii) minimizing the Frobenius norm of the resulting controller gain. The shifting of the uncontrollable mode is discussed in some detail. A scheme for determining the minimum Frobenious norm of the resultant state‐feedback matrix gain is developed. Finally, a numerical example is used for illustration of the proposed method.